Exeter beat Gloucester with a try bonus point in a brilliant game at Kingsholm, but missed out on top spot in the Aviva Premiership after Wasps beat Saracens.
Tries from centre Ian Whitten, prop Ben Moon, wing James Short and replacement Will Chudley plus two penalties and four conversions from fly-half Gareth Steenson were enough for the Chiefs to win 34-20.
But Gloucester never gave up and went over for three tries as England wing Jonny May got two and flanker Lewis Ludlow added another. Scrum-half Greig Laidlaw booted a penalty and conversion.
Wasps' 35-15 victory over Saracens mean they will play Leicester at home in the semi-finals, while the Chiefs will host Saracens.
Gloucester now have to beat Stade Francais in the European Challenge Cup final next weekend for a place in the Champions Cup play-offs and from the first minute to the last, it was high-octane stuff.
The Cherry and Whites started on fire as full-back James Hook fed Ludlow with an inside pass for a corner touchdown, and only a try-saving interception from scrum-half Stuart Townsend prevented Gloucester's second try in the 12th minute by fly-half Billy Twelvetrees.
It looked like Gloucester were the ones going for the Premiership top spot rather than their opponents but the match was building into a cracker when Exeter chipped away at the home team's 10-0 lead.
Three mistakes saw Steenson complete two penalties, but the third was surprisingly missed by the Chiefs fly-half in front of the posts. Steenson's despair deepened when he threw a pass on the Gloucester 10-metre line intended for wing Olly Woodburn.
However, it was wrestled away from the Exeter man by England wing May, who sprinted all the way to the Exeter line. It was the seventh interception try given away by Exeter in six games, but the Chiefs hit back quickly when Townsend fed Whitten with the ball from a ruck near the home 22.
There did not seem to be anything on but Whitten found his way past the defence and raced over unopposed from 25 metres for Steenson to convert from point-blank range.
It left the match nicely poised at 15-13 at the break, and there was no let-up in the excitement after the interval when May went over spectacularly but the 'try' was brought back for a knock-on.
Two tries in four minutes saw Exeter take the lead for the first time when Moon was put over by Sam Simmonds and Simmonds then supplied the pass for Short to score. It put Exeter 27-15 ahead but Gloucester would not give up and May went over again after sustained home pressure.
Back came Exeter as only some outstanding defence from the Cherry and Whites on their own line kept Exeter out until replacement Chudley stole over for the bonus-point try that Steenson converted, and that was enough for Exeter to end with 15 Premiership wins.