Bengaluru posted 218-5 after Du Plessis, who hit 54, and Kohli, who smashed 47, laid the foundations for the total in a rain-hit innings at their home M. Chinnaswamy Stadium.
Chennai were held to 191-7 in reply and with both sides level on 14 points, Bengaluru went through to the play-offs on run-rate after a sixth win in a row.
"What a night! Such a great atmosphere," player of the match Du Plessis, who did a lap of honour with his team for the home fans, said.
"Just a pleasure to finish the season in front of the home crowd with a win."
Bengaluru will now play in the eliminator on Wednesday in Ahmedabad.
Table-toppers Kolkata Knight Riders, Rajasthan Royals and Sunrisers Hyderabad had already made the play-offs, which will begin with the first qualifier on Tuesday in Ahmedabad.
The final is on May 26 in Chennai.
Rachin Ravindra hit 61 before Ravindra Jadeja, who made an unbeaten 42, and old warhorse M.S. Dhoni (25) gave Bengaluru a scare in a stand of 61 as Chennai fell short of the qualification mark.
The match could be Dhoni's last IPL outing as a player and also the final face-off between him and Kohli -- two legends of Indian cricket.
Dhoni, 42, was widely expected to retire after he led the team to a record-equalling fifth title last year, but vowed to come back for one more season after a knee operation.
Dhoni handed over the Chennai captaincy ahead of the season to Ruturaj Gaikwad, who won the toss and elected to field first in the virtual knockout for the final play-off place.
"Happy with the seven wins, couldn't get over the line though," said a disappointed Gaikwad.
Du Plessis stunner
Kohli, who leads the batting chart with 708 runs, and Du Plessis started on the offensive before rain halted their charge after the third over and suddenly the ball began to turn once play resumed.
Both openers waded their way through Chennai's spin charge from Maheesh Theekshana and Mitchell Santner as Kohli hit a couple of sixes.
New Zealand's Santner, a left-arm spinner, denied Kohli his fifty and got Du Plessis run out through a deflection from his finger at the non-strikers end.
Rajat Patidar, who hit 41, and Cameron Green, who struck an unbeaten 17-ball 38, then steadied the ship and hit back in a partnership of 71 off 28 balls.
Bengaluru returned strong with the ball and Glenn Maxwell struck on the first ball to send back Gaikwad for a duck.
Fast bowler Yash Dayal had Daryl Mitchell caught by Kohli to dent their chase.
But it was Du Plessis who pulled off a stunning one-handed airborne grab at mid-off to send back Santner.
Jadeja and Dhoni raised hopes of a turnaround as Chennai needed 17 off the last over to qualify but Dayal kept his calm to dismiss Dhoni and then gave away just one run.
