Charles made a 21-ball 40 opening the batting including four fours and two sixes while skipper Powell, batting at five, hit 35 off just 15 balls including one four and four sixes to help the Bulls post an intimidating 126-6 off their 10 overs after being put in to bat.
Englishman James Vince also showed good form with 37 off 14 balls. Obed McCoy and Junaid Siddique had identical figures of 2-18 from two overs.
Chennai’s chase then came up significantly short, being bowled out for just 61 in 8.5 overs.
Only Mohammad Nabi was able to crack double figures with 25 as Fazalhaq Farooqi (2-8 from two overs), Muhammad Rohid (2-14 from two overs), Naveen-ul-Haq (2-22 from two overs) and Ravi Bopara (2-4 from five balls) combined to produce an excellent display of bowling.
The win was Bulls' third in a row, and placed them comfortably at the top of the table, at least for the time being.
Tigers were going fine at 28 for 2 after three overs, and with Jordan Cox, David Miller and Dasun Shanaka, among others, to follow, looked set to put up another big total after scoring 143 for 4 in their win over Dubai Gladiators on Thursday.
But Gleeson changed the script in the space of five balls in the fourth over, getting rid of Miller, Shanaka and Cox, in that order, to leave Tigers completely off-kilter at 29 for 5.
Between Daniel Sams (20 not out in 15 balls) and Carlos Brathwaite (21 in 17), Tigers did fight back to get to 81 for 7, but it was never going to be enough against Bulls' powerful batting line-up.
Quinton de Kock and Johnson Charles fell inside two overs, but James Vince (17 in nine), Rilee Rossouw (21* in 11) and captain Rovman Powell (37* in 11) made sure Bulls got to the target quickly - in just six overs.
For Tigers, it was a second loss in three games, and at the end of it, they were placed seventh on the eight-team table.
Earlier on Saturday, explosive 30s from captain Nicholas Pooran and Tom Kohler-Cadmore, followed by Andre Fletcher's 12-ball 41, set up a crushing win for Deccan Gladiators over Team Abu Dhabi.
Pooran dashed out of the blocks taking left-arm finger-spinner Roelof van der Merwe for two fours and two sixes in the first over. Rumman Raees then dealt a double-blow, removing both Pooran and Andre Russell off successive balls in the fourth over, but Kohler-Cadmore and Fletcher proceeded to re-establish Gladiators' dominance.
Six of the 12 balls that Fletcher faced were sent to the boundary, including five sixes. Fletcher, Fabian Allen and Kohler-Cadmore all fell in quick succession, but David Wiese provided the final flourish with 15 off six balls.
Abu Dhabi started their chase shakily, losing their top three inside five overs. Leus du Plooy (25), Colin Ingram (19) and captain Dwaine Pretorius (9), fought back to lend some respectability to the scorecard. Sri Lankan slinger Nuwan Thushara, who plays for Jaffna Kings in the LPL, was the pick of the bowlers for Gladiators, coming away with 2 for 5 in his two overs.
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The Emirates’ innings got off to the worst possible start with openers Muhammad Wasim (5) and Vritiya Aravind (3) being removed within the first three overs after the Vipers won the toss and elected to field first.
Grenadian Andre Fletcher and former West Indies captain Nicholas Pooran then combined to put on 43 for the third wicket before Fletcher fell in the ninth over for 21 to leave them 53-3.
Captain Kieron Pollard then joined Pooran at the crease and the pair batted excellently, eventually bringing up their 100-run partnership in the 19th over, the same over which saw Pooran bring up a well-compiled 50.
Pollard brought up his 50, his second in a row, in the previous over with a trademark straight six.
The partnership reached 116 when Pooran was finally dismissed, bowled by Tom Curran in the final over for 57.
In the end, the Emirates closed their innings 169-5 off 20 overs with Pollard not out on 67 from 39 balls including one boundary and six sixes.
The Vipers chase was rocked early when Trent Boult removed Rohan Mustafa for one in the first over to bring captain Collin Munro to the crease.
Hales and Munro put on a partnership before Munro was removed by a spectacular catch from Kieron Pollard for 41 in the eighth over.
One brought two for the Emirates as Samit Patel got his second wicket in the over, removing Sam Billings for just one to leave the Vipers 76-3 bringing Sherfane Rutherford to the crease.
At the halfway stage of the chase, the Vipers were 101-3 with Hales (34) and Rutherford (18) going smoothly.
The pair continued along and Hales brought up his fifth score of 50+ in a row in the 15th over before a single in the 16th over brought up Rutherford’s 50 off just 26 balls.
The match was ended in the 17th over when Rutherford hit a boundary and then a single to lead the Vipers to their fourth win in five games.
Hales ended up unbeaten on 62 from 44 balls while Rutherford faced 29 balls for his 56. Hales’ knock included six fours and two sixes while Rutherford hit four fours and three sixes.
Scores: MI Emirates 169-5 from 20 overs, Desert Vipers 170-3 from 17.3 overs.
Defending 121, the Strikers' left-arm spinner picked up a hat-trick in the first over of the innings, dismissing Andries Gous, Dewald Brevis and Ibrahim Zadran, to leave Samp Army reeling at 1 for 3.
In his second over, he removed the opposition captain Faf du Plessis and Najibullah Zadran in space of three balls to further rattle Samp Army.
Jason Holder's 22 of 11 and Qais Ahmad's unbeaten 31 off 13 at No.10 meant Samp Army huffed and puffed to 80 for 9.
Earlier, opener Rahmanullah Gurbaz's blazing 56 off 28 set the tone for Strikers to post a competitive 121 for 5. His knock included four fours and five sixes.
In the end, Asif Ali smashed three fours in his unbeaten seven-ball knock of 17 to further lift Strikers.
Samp Army will have a second chance to make the final when they play the winner of the Eliminator between Bangla Tigers and Deccan Gladiators in Qualifier 2 later today.
At the time of publishing, the Tigers were 78-4 off seven overs batting first.
If you score 98 for 4 in a ten-overs-a-side tournament where three figures are breached quite often, you expect to have it tough in the second half, but it was certainly not the case on the day for Strikers at the Zayed Cricket Stadium on Monday.
Two wickets fell in the first over of the chase, to Akeal Hosein (3 for 7), one each in the second and third, and three in the fifth to Chamika Karunaratne (3 for 6). That was the end of the specialist batters bar Bopara, who was the only Bulls batter to get into double-digits with 16.
The Bulls were bowled out with three balls left in the innings after four batters fell for ducks.
In the first half, Rahmanullah Gurbaz dominated proceedings with a 24-ball 49 not out, as Strikers reached what was a just-about-par score of 98… it proved more than three times what Bulls could manage on the day.
Bulls have now lost two on the bounce after starting with three wins in a row, and are still up at No. 3 on the table, while Strikers, after starting with a loss, have now won three in a row.