Virat Kohli suffered more heartbreak on Wednesday as Royal Challengers Bengaluru were knocked out of the IPL after a four-wicket loss to Rajasthan Royals in Ahmedabad.

Rajasthan restricted Bengaluru to 172-8, a total they overhauled with six balls to spare in the do-or-die play-off at the world's biggest cricket stadium.

Bengaluru and Kohli extend their wait for a first IPL title. Rajasthan will face Sunrisers Hyderabad in the last play-off on Friday in Chennai to decide Kolkata Knight Riders' opponent in the final on May 26.

Kolkata made their fourth IPL final after they hammered Hyderabad in the first play-off on Tuesday in Ahmedabad's intense heat.

Trent Boult, with figures of 1-16, and Ravichandran Ashwin, 2-19, played pivotal roles in a disciplined bowling attack for Rajasthan, who elected to field first.

Rajasthan stuttered in their chase after Yashasvi Jaiswal, caught behind off Cameron Green on 45, and skipper Sanju Samson, stumped out for 17, departed in the space of five deliveries.

Riyan Parag, who hit 36, and Shimron Hetmyer, who smashed 26, put on 45 to get their chase back on track before Rovman Powell steered the team home with a six in his unbeaten 16.

Rajasthan, who won the inaugural edition of the IPL in 2008 under late Australian legend Shane Warne, bounced back from four losses in five matches including a washout.

Bengaluru's dream run ended after they rose from the bottom of the table after eight matches to win six in a row and make the play-offs.

Ahmedabad remained hot as temperatures in the afternoon soared above 43 degrees Celsius (109 degrees Fahrenheit) for the third successive day.

There was a sea of Kohli fans who braved the heat and stadium officials said over 85,000 people turned up for the eliminator.

Substitutes ran with towels and water bottles all around outside the boundary ropes to keep their players on the field hydrated.

Most of India's northern states have remained under government heatwave alerts since last week.

According to local reports, Bollywood actor and IPL team owner Shah Rukh Khan was hospitalised in Ahmedabad due to a heatstroke a day after he celebrated Kolkata's victory at the venue.

Earlier, skipper Faf du Plessis departed early on 17 after Powell took a stunning forward diving catch running from deep mid-wicket off left-arm quick Boult.

Kohli attempted to set the pace in his 24-ball 33 but fell to Yuzvendra Chahal's leg-spin, much to the disappointment of the crowd at the 132,000 capacity stadium.

Kohli consolidated his position as the season's leading batsman with 741 runs including a century and five half tons in 15 matches.

Rajasthan bowlers kept a check on the scoring and took regular wickets including two off successive balls when off-spinner Ashwin sent back Green, for 27, and Glenn Maxwell, for a duck.