Harlequins claimed a priceless bonus-point victory over Exeter on Sunday, winning 30-29 in a result that boosts their hopes of making the top four.
Dave Lewis' converted try and three Gareth Steenson penalties took Exeter into a 16-5 lead at the interval, while the London-based outfit's response came through Ugo Monye's touchdown.
Matt Jess crossed the whitewash in the second-half to increase the Chiefs' advantage before Quins mounted a comeback with Nick Evans going over and adding two penalties from the tee.
Steenson's three-pointer eased the pressure slightly, but Danny Care's score brought the away side to within one point.
The hosts thought they might have won it with another effort from the boot of their fly-half, but Guest went over to snatch the win and set up a winner-takes-all decider versus Bath.
Following the West Country outfit's 19-19 draw with Northampton Saints on Friday, it gave the visitors an excellent chance of closing the gap and keeping themselves in contention for a play-off place.
Against a team that had lost their previous encounter 55-12 at home - their heaviest defeat in the Premiership - it only increased the odds in Quins' favour.
However, the West Country outfit were massively improved from their last match and they moved into an early 10-0 lead.
Steenson opened the scoring via a penalty before a powerful rolling maul gave Lewis the space he needed to scamper over.
Although Monye's excellent finish, following a superb off-load by Dave Ward, reduced the arrears to 10-5, successive three-pointers by the Exeter fly-half increased the hosts' advantage to 16-5.
The visitors needed a response but it was the Chiefs that started the second half the brighter and an outstanding break by Ian Whitten led to Jess crossing the whitewash for a brilliant score.
Evans' well-taken try moved Harlequins back into contention and a yellow card for Damian Welch increased the pressure on the home side's rearguard.
Quins' pivot kicked the resultant opportunity from the tee before adding another just a few minutes later to move them to within five points.
The momentum was very much with the visitors and, despite Steenson scoring a penalty, Charlie Matthews, Joe Marler and Nick Easter combined to send Care over.
Steenson's fifth penalty made the score 29-25 in Exeter's favour, but there was a late twist when Ward's off-load gave Tom Guest an easy finish to seal the win.
Tries: Lewis, Jess
Con: Steenson 2
Pen: Steenson 5
Tries: Monye, Evans, Care, Guest
Con: Evans 2
Pen: Evans 2
Exeter: 15 Phil Dollman, 14 Fetu'u Vainikolo, 13 Ian Whitten, 12 Sam Hill, 11 Matt Jess, 10 Gareth Steenson, 9 Dave Lewis, 8 Kai Horstmann, 7 Ben White, 6 Dave Ewers, 5 Damian Welch, 4 Dean Mumm (capt), 3 Hoani Tui, 2 Luke Cowan-Dickie, 1 Carl Rimmer.
Replacements: 16 Jack Yeandle, 17 Craig Mitchell, 18 Alex Brown, 19 James Phillips, 20 James Scaysbrook, 21 Haydn Thomas, 22 Henry Slade, 23 Tom James.
Harlequins: 15 Mike Brown, 14 Tom Williams, 13 Tim Molenaar, 12 Jordan Turner-Hall, 11 Sam Smith, 10 Nick Evans, 9 Danny Care, 8 Nick Easter, 7 Chris Robshaw (c), 6 Luke Wallace, 5 Nick Kennedy, 4 Charlie Matthews, 3 Kyle Sinckler, 2 Dave Ward, 1 Joe Marler.
Replacements: 16 Rob Buchanan, 17 Mark Lambert, 18 Paul Doran Jones, 19 Tom Guest, 20 Maurie Fa'asavalu, 21 Ben Botica, 23 Ugo Monye.
Referee: Andrew Small
Assistant referees: Stuart Terheege, Peter Huckle
Television match official: Greg Garner