RCB first posted 173-6 from their 20 overs after winning the toss.
Wicket-keeper/batsman Anuj Rawat top scored with a 25-ball 48 while Dinesh Karthik and captain Faf Du Plessis provided good support with 38 and 35, respectively.
Mustafizur Rahman was excellent with the ball for the Super Kings with 4-29 from his four overs.
CSK then used contributions from all their batsmen to easily reach 176-4 with eight balls to spare.
Debutant Rachin Ravindra led the way with 37 while Shivam Dube (34*), Ajinkya Rahane (27) and Ravindra Jadeja (25*) also played well.
Cameron Green took 2-27 from his three overs for RCB.
Full Scores: Royal Challengers Bengaluru 173-6 off 20 overs (Anuj Rawat 48, Dinesh Karthik 38*, Mustafizur Rahman 4-29)
Chennai Super Kings 176-4 off 18.4 overs (Rachin Ravindra 37, Shivam Dube 34*, Ajinkya Rahane 27, Ravindra Jadeja 25*, Cameron Green 2-27)
Russell injured himself during the second over of the KXIP run chase, while trying to prevent a boundary. He attempted a sliding dive but failed to stop the ball and then crashed into into an advertisement board.
He was later seen icing the knee and eventually returned to the field in the eleventh over only to leave the field for good shortly thereafter.
Speaking after the game, KKR skipper Dinesh Karthik expressed concern over Russell, whom he described as a very special player.
“Whenever Russell gets injured, you know it is hard. He is a very special player, he is a very special person. We need to go and look at him,” Karthik said clearly concerned over whether Russell would be fit enough to start their next game on Monday when KKR plays the Royal Challengers Bangalore.
Dre Russ has struggled with the bat so far this season, scoring on 55 runs this season with a high score of 24. He has been carrying an issue with his knee since playing for the Jamaica Tallawahs in the CPL held earlier this year.
West Indian captain Nicholas Pooran won the toss and elected to field first.
India’s opening pair of returning captain Rohit Sharma and Suryakumar Yadav got the ball rolling, putting on a partnership of 44 before Yadav was dismissed by Jason Holder for a quick 16-ball 24.
Captain Sharma provided a steady head for the Indians throughout the majority of the innings as he lost partners Shreyas Iyer (0), Rishabh Pant (14) and Hardik Pandya (1) before eventually being dismissed in the 15th over for a top score of 64 to leave the tourists 127-5.
They eventually got up to 190-6 off their 20 overs thanks to cameos from Ravindra Jadeja (16) and Ravichandran Ashwin (13) as well as a brilliant closing effort of 41 from just 19 balls including four fours and two sixes from Dinesh Karthik.
Left-arm spinner Akeal Hosein was brilliant for the hosts with an economical 1-14 from his four overs while opening pacer Obed McCoy took 1-30 from his four.
The West Indian reply got off to a fast start thanks to openers Kyle Mayers and Shamarh Brooks as the pair sped to 22-0 in the second over before Mayers fell for 15 to pacer Arshdeep Singh.
The Windies then tried to gamble, sending Jason Holder up the order to bat at three but this move fell flat as he was next to go, bowled by Ravindra Jadeja for a duck.
The innings then ground to a virtual halt as Brooks (20), Nicholas Pooran (18), Rovman Powell (14), Shimron Hetmyer (14), Akeal Hosein (11) and Odean Smith (0) all perished to, eventually, leave the Windies needing 90 off 21 balls for victory.
Keemo Paul and Alzarri Joseph then finished not out on 19 and 5, respectively, to end the innings on 122-8, 68 runs short.
It was a balanced bowling effort by the Indians with Ravichandran Ashwin (2-22 off four overs), Arshdeep Singh (2-24 off four overs) and Ravi Bishnoi (2-26 off four overs) all contributing well.
After winning the toss and electing to field first, the hosts felt the wrath of the Indians from the outset with openers Rohit Sharma and Suryakumar Yadav speeding to 53 without loss after just 4.4 overs before Sharma was dismissed for a 16-ball 33 including two fours and three sixes.
Yadav’s dismissal for 24 in the sixth over then paired Deepak Hooda and Rishabh Pant who added a further 47 before Hooda’s wicket fell for 21 in the 12th over to leave the score on 108-3.
Pant went on to top-score with 44 before his dismissal in the 15th over. Sanju Samson (30 not out), Axar Patel (20 not out) and Dinesh Karthik (6) then combined to put the finishing touches on a fine effort with the bat for India, ending 191-5 from their 20 overs.
Alzarri Joseph was the pick of the bowlers for the Windies with 2-29 from his four overs.
The hosts then struggled throughout their reply thanks to some excellent bowling by India and some questionable decision-making by the batsmen.
Brandon King (13) and Kyle Mayers (14) both got starts but fell cheaply while captain Nicholas Pooran sprinted to 24 off just eight balls before he was run out after a mix-up with Mayers.
Rovman Powell with a quick 24, Shimron Hetmyer (19) and Jason Holder (13) were the only other batsmen to reach double-figures as the Windies struggled to a paltry 132 all-out after 19.1 overs.
Arshdeep Singh led the way for the Indians with 3-12 from 3.1 overs while he got good support from Avesh Khan (2-17) and Ravi Bishnoi (2-27).