After a breathtaking 104 from Klaasen that lit up the Uppal Stadium, Kohli and Faf du Plessis put on their superhero capes as the duo made a mockery of the 187 chase.
Firing the highest partnership of the season, Kohli and du Plessis added 172 runs for the opening wicket as Bangalore cruised to their seventh win and sneaked into the top four, pushing Mumbai Indians to the fifth.
Slamming his sixth century and first since 2019, batting virtuoso Kohli also equalled Chris Gayle’s record of hitting most hundreds in the biggest cricket league in the world.
After Kohli and du Plessis’ mammoth fourth century-plus partnership, Glenn Maxwell and Michael Bracewell wrapped up the chase with 4 balls to spare.
Klaasen displayed his big-hitting prowess, slamming six sixes and eight fours during his scintillating 51-ball 104-run knock to lift SRH to 186 for five from 28 for 2 in the fifth over.
But Kohli (100) had other plans as he and du Plessis (71) helped RCB chase down the target with their magnificent ball-striking on way to a record-breaking opening stand.
RCB are now at no.4 on the table due to their better net run rate although they are tied with Mumbai on 14 points. They will, however, have to win their next match to stay in the mix as Chennai Super Kings and Lucknow Super Giants are at 15 points with one match to go.
Kohli was all class as he hit four maximums and 12 fours in his 63-ball knock, while du Plessis cracked seven fours and two sixes in his 47-ball knock as the two dished out a chasing masterclass.
Often criticised for slowing down post the powerplay, Kohli settled the debate with some extraordinary shots as he kept dealing in boundaries in the middle overs to never let the tempo slip.
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Needing a win to stay in play-off contention, Kohli and du Plessis gave RCB a flying start to their chase. The in-form opening duo played some gorgeous shots, piling up 64 in the first six overs.
Kohli started the proceedings with two hits across the ropes off Bhuvneshwar Kumar, before slamming spinner Abhishek Sharma for two more boundaries.
The skipper then joined the party, punishing Kartik Tyagi for bowling short with three fours though he was dropped by Glenn Phillips in between at the boundary line.
Kohli then played an exquisite shot at deep extra cover for another four as 18 runs came off the fourth over.
Du Plessis next deposited Bhuvneshwar over deep square leg and followed it up with another four with RCB accumulating 14 runs off the over.
Knowing well that net run rate might come into play to decide the top four, Kohli and du Plessis kept their foot on the pedal with the former pulling debutant Nitish Reddy over deep mid.
Mayank Dagar pulled off an unbelievable catch at the boundary line but du Plessis survived after umpire called it a no-ball as Nitish was guilty of bowling a second bouncer.
After two quiet overs, du Plessis blasted Abhishek for a six and a four, before Bhuvneshwar came in the firing line, conceding four boundaries as the 15th over yielded 18 runs.
Kohli completed his hundred with another six off Bhuvneshwar before holing out in the next ball. Du Plessis followed suit with T Natarajan’s slower delivery doing the trick.
Glenn Maxwell and Michael Bracewell then completed the job.
Earlier, Klaasen forged a 76-run partnership with Aiden Markram (18) before adding another 74 off 36 balls with Harry Brook (27 not out) to take SRH to a competitive total.
Already out of playoff race, SRH once again had a poor start with Rahul Tripathi (15) and Abhishek Sharma (11) frittering away good starts.
It was off-spinner Michael Bracewell who struck twice, removing both the openers in his first three balls. While Abhishek hit straight to Lomror at cover, Tripathi found the fine leg fielder off his slog paddle sweep.
Klaasen hammered three fours off Shahbaz Ahmed to power the Sunrisers to 49 for 2 in the powerplay.
Klassen rocked back and pulled every time the ball was short as Bracewell and Harshal Patel was sent across the ropes, while Karn Sharma was dispatched for a 74-metre six.
Karn Sharma was then punished for bowling over-pitched with Klaasen depositing him into the stands. The South African completed his fifty in 24 balls.
While Klaasen was in full flow, Markram managed just run-a-ball 18 before his off stump was pegged back by Shahbaz while he looked for a reverse hit.
Brook then picked up a four and six off Karn Sharma, who bled 21 runs, with Klaasen too lifting him over cover.
Du Plessis’ decision to make Shahbaz bowl the 17th over backfired as Klaasen clobbered the first two balls over the bowler’s head, while Brook sent one fine.
Parnell nailed the yorkers to concede just seven runs in the next over but Klaasen then plundered Harshal over his head to bring up his hundred. He was dismissed one ball latter while looking for another big shot.
(With inputs from PTI)
Watch IPL: Kohli, du Plessis show keep RCB in play-off hunt