Kumar left the Royals reeling at 1-2 as they chased 202 for victory, dismissing both Jos Buttler and Sanju Samson for first-over ducks, flattening middle wicket to send the latter walking five balls in.
A 127-run partnership between Yashasvi Jaiswal and Riyan Parag then seemed to have the Royals closing in on a fifth straight win, only for their chase to unravel in spectacular fashion.
Two wickets apiece from Thangarasu Natarajan and Pat Cummins left the Royals needing 20 runs off 11 balls, and Rovman Powell came up with a thrilling cameo, the highlight being an unbelievable dive to avoid being run out on the penultimate delivery, which took Rajasthan within two runs of victory and one of a super over.
However, there was one more twist to come as Powell swung at Kumar's full toss, which clipped his back leg and was confirmed as out following a review, sealing a memorable win for Sunrisers.
The Sunrisers had also found themselves in a hole in their own innings, only for Nitish Kumar Reddy (76) and Heinrich Klaasen (42) to finish unbeaten and bring up a total they were just about able to defend.
Data Debrief: Kumar bookends back-and-forth innings
For much of the Rajasthan innings, it looked like Kumar's early dismissals of Buttler and Samson would count for nought, with some expensive overs from Cummins and Marco Jansen leaving the Royals on the brink.
However, Kumar stepped up when it was all on the line on the final delivery, leaving Powell in a tangle to end Hyderabad's two-match losing streak and lift them into the top four.
Ishan Kishan (34) and Shreyas Iyer (40) offered India a bright start at the Barabati Stadium on Sunday.
But the hosts' middle-order batters struggled before Dinesh Karthik scored a brisk 30 off 21 balls to propel India to 148-6.
Having chased an improbable 212 in the first meeting, South Africa initially struggled this time around with Bhuvneshwar Kumar reducing the tourists to 29-3 after an opening spell of three wickets for 10 runs.
Captain Temba Bavuma watched as wickets fell around him but posted an important 35 before being bowled by Yuzvendra Chahal (1-49).
Bavuma combined in a vital 64-run partnership with Klaasen, whose brutal 81 came off just 46 deliveries before he was removed by Harshal Patel (1-17) and Wayne Parnell (one) fell to Kumar (4-13).
David Miller (20 not out) then saw South Africa over the line with 10 balls to spare as the Proteas furthered their advantage in the five-match series.
Rapid Rabada
Rabada became the fourth South African bowler to claim 50 wickets in men's T20Is when he dismissed Ruturaj Gaikwad for one in the first over.
The fast bowler achieved the feat in his 42nd game, making him the third-fastest bowler from South Africa to a half-century of dismissals, behind only Dale Steyn (35) and Imran Tahir (31).
Hendricks misses opportunity
Chasing a far from imposing total, Reeza Hendricks had the chance to make his mark as an opener, replacing South Africa stalwart Quinton de Kock.
However, the 32-year-old made just four before being bowled by Kumar as he failed to leave a lasting impression in a rare opportunity at the top of the order.
India posted 164-5 after they were asked to bat first in Colombo, with skipper Shikhar Dhawan's 46 and a 34-ball 50 from Suryakumar Yadav providing the bulk of the runs.
Dushmantha Chameera (2-24) and Wanindu Hasaranga (2-28) did the damage for Sri Lanka, but the majority of the home side's batsmen failed to fire after the interval.
Avishka Fernando (26) and Charith Asalanka (44) briefly gave Sri Lanka some hope, but Kumar (4-22) and Deepak Chahar (2-24) got the job done as the hosts were bowled out for 126 with nine balls to spare.
Sri Lanka were outclassed in their recent T20I series in England, which ended in a 3-0 loss, but even on home soil Mickey Arthur's side lack the batting firepower and they have now won just once in their previous 14 completed fixtures.
The second and third Twenty20 internationals in Colombo, both also at the R. Premadasa Stadium, take place on Tuesday and Thursday as both sides continue their preparations for the T20 World Cup later this year.
Kumar closes in on milestone
India seamer Kumar was cool during the business end of the match as he took three of the final four wickets to fall. He needs just one wicket to reach 50 in T20I action for India and become the fourth player to achieve this feat for the country.
Shanaka must deliver more
Sri Lanka lost their final six wickets for less than 15 runs and needed more from T20 captain Dasun Shanaka, who made a tame 14-ball 16. Shanaka is normally an aggressive middle-order batsman but his modest innings included just one four before he was stumped off the bowling of debutant Varun Chakravarthy.
Jennings (112) made the most of some early fortune in Mumbai, being dropped on nought by Karun Nair and also surviving a close umpire’s call for lbw against Bhuvneshwar Kumar, on his way to a 186-ball hundred.
It was a contribution which looked to have put England ahead of the game as they reached 288 for five at stumps after Alastair Cook won a crucial toss.
However, after making exactly 400 in their first innings, England ultimately lost by an innings and 36 runs as they were bowled out for 195 on their second attempt after the home side made a mammoth 631 in their first innings.
That meant England became only the third team in Test history to lose a match by an innings after making 400 or more first time round.
Jennings was assured after his early scrapes and hit 13 boundaries in stands of 99 with Cook and 94 with Moeen Ali (50) as England negotiated the wiles of spinner Ravi Ashwin (four for 75).
Jennings completed his hundred with a reverse-swept four off Jayant Yadav as he put England in a position of promise as they sought to battle back from 2-0 down with two Tests to play.
The South Africa-born batter went on to play a total of 17 Tests for England, the last of which came against West Indies in February 2019.
Jennings was appointed Lancashire captain in all three formats for the 2023 season.
The world's top-ranked T20I side recorded a 10th consecutive victory in Lucknow, as they continue to build towards the T20 World Cup in Australia.
Ishan Kishan scored a majestic 89 off 56 in a superb display from India's top order saw in which the hosts reached 199-2 in their 20 overs, before Bhuvneshwar Kumar was a star turn with the ball to help wrap up a comprehensive win.
India were sent out to bat after visiting skipper Dasun Shanaka won the toss and racked up 50 runs in just over five overs.
Captain Rohit's (44 off 32) landmark moment arrived when he smashed Jeffrey Vandersay's delivery for six in the eighth over, as he and fellow opener Kishan toyed with the Sri Lankan bowlers.
Star man Ishan reached his half-century off just 30 balls, as the hosts passed the hundred mark before suffering their first loss of the contest, Rohit being beaten by Lahiru Kumara's delivery.
Ishan was finally caught by Janith Liyanage, with the visitors unable to claim any further wickets before the 20 overs were through.
India were equally dominant with the ball. Bhuvneshwar Kumara struck with the first delivery to wipe out Pathum Nissanka and followed up by dismissing Kamil Mishara (13 off 12) inside three overs.
Venkatesh Iyer and Ravindra Jadeja joined the party shortly afterwards, while Yuzvendra Chahal removed Shanaka (3) for the fifth, becoming India's leading T20I wicket taker with his 67th dismissal in the format.
Sri Lanka's Charith Asalanka hit 53 off 47 balls, but it was not enough to avoid a comprehensive beating for the visitors, who fell to a 1-0 series deficit.
India skipper enters the record books
Rohit Sharma took the title of all-time leading run-scorer in T20I cricket, surpassing New Zealand's Guptill and fellow India star Kohli with his haul of 44 from 32 balls.
That return takes him to a total of 3,307 runs in the T20I format, a tally he will doubt add to in the remainder of the series.
Home bowlers target records of their own
Chahal's dismissal of Sri Lanka skipper Shanaka, meanwhile, made him India' most prolific bowler in the T20I format, with 67 wickets in his 53 matches.
Bhuvneshwar Kumar, meanwhile, is fourth on that list after wreaking havoc upon the Sri Lankan bowling order, claiming 57 T20I wickets since his 2012 debut.
Roy hit 44 as the Sunrisers, who sit bottom of the table with their play-off hopes already over, earned only their third win of a torrid Indian Premier League season at the Sheikh Zayed Stadium.
Already assured of a play-off berth, RCB were aiming for a fourth successive victory that would strengthen their hopes of finishing in the top two.
Virat Kohli's side were set a target of 142 and headed into the final over needing 13, following knocks of 41 and 40 from Devdutt Padikkal and Glenn Maxwell respectively.
AB de Villiers, who finished on 19 not out, edged RCB closer to the total with a huge six off Bhuvneshwar Kumar's fourth ball of the final over to leave six required from the last two deliveries.
However, Kumar showed all of his experience to wrap up the victory, conceding just one run off his final two balls, as RCB fell narrowly short on 137-6.
Joy for Roy
The England opener made a top-scoring contribution for the Sunrisers, with a knock of 44 from 38 balls.
He and skipper Kane Williamson hit combined in a 70-run partnership in 9.4 overs to provide the platform for their side to build upon.
History for Patel
Despite the defeat, it was a historic day for Harshal Patel, who set a new record of most wickets by an Indian bowler in an IPL season as he surpassed Jasprit Bumrah's tally from the previous season (27).
The right-arm bowler claimed an impressive 3-33 as he dismissed Williamson, Wriddhiman Saha and Jason Holder.
That took Patel's tally in this season's IPL to 29; seven clear of nearest challenger Avesh Khan, who has impressed for the Delhi Capitals this term.
The start of the series was delayed by five days due to a coronavirus outbreak in the Sri Lanka camp, with batting coach Grant Flower and team data analyst GT Niroshan testing positive for the Delta variant.
Sri Lanka's squad were allowed to leave isolation and resume their preparations last weekend after returning negative PCR tests.
ESPNcricinfo reported team doctors believed Flower and Niroshan's infections stemmed from the recent tour of England, where the home team suffered a breach of their bio-secure bubble that forced them to name a reserve line-up for their subsequent ODI games against Pakistan.
Although Sri Lanka do not find themselves in quite such a selection bind, they remain without deposed captain Kusal Perera due to a shoulder injury and Niroshan Dickwella, Kusal Mendis and Danushka Gunathilaka remain suspended for breaking COVID-19 protocols during the England tour.
Dasun Shanaka will skipper the team, a previously bit-part white ball player having ascended to the role amid a stand-off between Sri Lanka's players and their board over playing contracts.
They will emerge from a troubled period to take on an India side captained by opener Shikhar Dhawan and with pace bowler Bhuvneshwar Kumar second in command.
India batting great Rahul Dravid has been named as coach for the tour, with the first-choice side awaiting their forthcoming series in England.
Batsmen Devdutt Padikkal, Ruturaj Gaikwad and Nitish Rana, all-rounder K Gowtham and left-arm seamer Chetan Sakariya have all been handed maiden call-ups.
Bhuvi ready to put injury woes to one side
Kumar will be the leader of fast bowling unit also featuring Sakariya, Navdeep Saini and Deepak Chahar. Having been beset by injury problems over recent years, he was back to his best in the March limited-overs series against England. In the ODIs, he took six wickets at a miserly economy rate of 4.65.
Shanaka must show leadership class
Irrespective of how and why Shanaka became Sri Lanka captain, he is now the man in possession of a role that tends not to promise longevity for incumbents. He will need to improve upon 611 runs and 10 wickets from his 28 ODI appearances to date to turn some unhelpful conversations around.
Key Opta facts
- India are undefeated in their past 11 ODI series against Sri Lanka (W9, D2). Their previous defeat was a 3-0 reverse way back in 1997.
- India have won each of eight most recent ODIs in Sri Lanka, all versus the host country. It is a streak that began after a nine-wicket loss in 2012.
- Sri Lanka have at least won their past five ODIs at the R. Premadasa Stadium. The last time they enjoyed a longer winning run at the venue in this format was a six-match span from December 2001 to September 2002.
- Dhawan will become the 25th player to captain India in ODIs. He requires 23 more runs to become the 10th Indian player to register 6,000 runs in 50-over internationals.
The tourists will have to bounce back quickly ahead of Thursday's decider having come up just short of a victory that would have secured a fourth successive bilateral series success against Sri Lanka in this format.
Krunal Pandya's positive COVID-19 test prompted the postponement of this match on Tuesday and ruled out eight players as close contacts.
That meant there were four debutants in the India XI, with Ruturaj Gaikwad opening in a depleted batting line-up and Devdutt Padikkal coming in at number three, and Sri Lanka capitalised.
India made a promising start, but were restricted to 132-5 after being asked to bat first, captain Shikhar Dhawan top scoring with 40.
Although Minod Bhanuka (36) departed quickly after he was dropped by Bhuvneshwar Kumar, Sri Lanka remained within reach heading into the closing stages of their chase.
A brief late rain delay dragged out the drama and Sri Lanka – led by Dhananjaya de Silva (40 not out) – then immediately profited from a 12-run 19th over that brought them within eight, a target achieved with two balls to spare.
HERO TO ZERO
This should have been a night to remember for Bhuvneshwar, whose unbeaten career-high 13 in India's innings – batting up the order at six – was followed by his 50th wicket in the format. He is the fourth Indian bowler to this mark.
But, as well as that awful drop, he was the man running in for the 19th over, with Sri Lanka in complete control after Chamika Karunaratne hit a full toss for six.
TOUGH GROUNDING
For a time, it had appeared as though Bhuvneshwar was setting an example for Chetan Sakariya, the debutant seamer who struggled from the outset. Ultimately, they both contributed to India's defeat.
Starting alongside Bhuvneshwar in the attack, there were nine runs off Sakariya's first over and 10 off the second. A first wicket came in the third as Ramesh Mendis paid for his aggressive approach, but that over still brought eight and the miserable fourth saw Sri Lanka seal victory. Sakariya went for 34 off 3.4 overs.
Kohli's magnificent unbeaten 82 gave India a dramatic win over Pakistan on Sunday and he followed that up with 62 from 44 balls as India posted 179-2 in Sydney on Thursday.
Captain Rohit Sharma struck 53 from 39 deliveries after being dropped by Tim Pringle on 13 and Suryakumar Yadav (51 not out off 25) also made a half-century to leave the Dutch facing a substantial run chase.
Netherlands never looked like pulling off a huge upset, falling short on 123-9 as they suffered defeat in as many Super 12 matches.
Bhuvneshwar Kumar (2-9) took the wicket of Vikramjit Singh and did not conceded a run in his first two overs, while Axar Patel (2-18), Ravichandran Ashwin (2-21) and Arshdeep Singh (2-37) also impressed with the ball.
Victory for India moved them a point ahead of South Africa, who hammered Bangladesh by 104 runs earlier in the day, at the top of Group 2.
Kohli goes back-to-back, Suryakumar shows his class
A Kohli masterclass gave India a sensational victory over Pakistan at the MCG and the former captain carried on where he left off in another classy knock.
He reached his half-century in 37 balls, hitting two sixes and finding the rope three times in another high-quality innings.
Suryakumar, number three in the T20I batting rankings, hit seven fours and reached his half-century by launching the final ball of the innings from Logan van Beek for six.
The brilliance of Bhuvneshwar
India also demonstrated the potency of their bowling attack and it was Bhuvneshwar who set the tone.
He bowled back-to-back maidens and cleaned up before returning to get rid of captain Scott Edwards in his second spell.
Punjab captain Dhawan, who was dropped twice by Bhuvneshwar Kumar, fell agonisingly short of three figures against his former side, blasting the last ball for six to drag the Kings to 143-9 in Hyderabad.
Mayank Markande had rattled through the Punjab batting line-up with an incredible 4-15 through the middle overs before Dhawan contributed to 52 of the 55-run last-wicket stand with Mohit Rathee (1 not out).
Sam Curran (22) was the only other Kings batter to hit double figures as Marco Jansen (2-16) and Umran Malik (2-32) impressed, although the Sunrisers allowed Punjab back into the game after they were 88-9.
Hyderabad made a stuttering start to their chase as Harry Brook fell for 13 when bowled by Arshdeep Singh (1-20) before Rahul Chahar (1-28) removed Mayank Agarwal (21) to leave the hosts 45-2 after 8.3 overs.
But Tripathi stepped up with an expert 74 from 48 deliveries, combining with Sunrisers skipper Aiden Markram (37 not out) in a vital 100-run partnership to see Hyderabad over the line with 17 balls left.
Bhuvneshwar sets early tone for Sunrisers
Bhuvneshwar (1-33) dismissed Prabhsimran Singh leg before wicket with the first ball of the match to set the tone, albeit his erroneous catching efforts afforded Dhawan two lifelines later in the Kings innings.
Veteran star Bhuvneshwar has dismissed an opening batter 55 times in the IPL, the most by any seamer in history and third among all bowlers (Ravichandran Ashwin and Harbhajan Singh have 61 each).
Non-existent support for remarkable Dhawan
Dhawan was left without support despite his incredible effort. He accounted for 69.2 per cent of his side's total, the second-highest percentage of a team's runs in IPL history when batting first (after Brendon McCullum scored 158 not out in Kolkata Knight Riders' 223 versus Royal Challengers Bangalore in 2008).
Opener Dhawan smashed 12 fours and cleared the ropes five times in his well-crafted 66-ball innings, becoming the leading run scorer in the embryonic IPL batting charts after taking his tally to 225.