Exeter took five Aviva Premiership points from a 38-33 victory at Worcester, although the home side came within a converted try of grabbing a dramatic win in a thrilling encounter.
Worcester were languishing 21-3 behind at one stage but fought back bravely to get two bonus points, through four tries and finishing within seven points of the Chiefs.
Scrum-half Dave Lewis, centre Sam Hill, fly-half Gareth Steenson and hooker Jack Yeandle got first-half tries for Exeter, while full-back Chris Pennell and David Lemi crossed for Worcester.
But the home side, bottom of the table and facing relegation, battled brilliantly in the second half through tries by hooker Agustin Creevy and Lemi's second against another Yeandle try.
Ryan Lamb kicked three penalties and two conversions as well while Steenson ended on 18 points by adding a penalty and five conversions to his touchdown.
Despite the Warriors' late fightback, the relegation trapdoor now seems wide open and they must have been fearing the worst after just 24 minutes as Exeter strolled past some weak defence to rack up three tries and that 21-3 lead.
Lewis raced over for the first after nine minutes as he nipped past home prop Ofa Fainga'anuku to race to the line, with Pennell forlornly chasing.
Steenson converted but Lamb added Worcester's opening points with a 40-metre penalty.
Hill's try soon followed as he was put over from two metres by his fly-half after an initial charge from Fetu'u Vainikolo, and with Steenson converting, Exeter's lead was stretched again.
It got worse for Worcester as Lamb missed another long-range attempt before Steenson rounded off another break into home territory for his own converted try.
The Worcester defence was almost non-existent and, when they had some possession inside the opposition 22, the Chiefs stood strong. It seemed how many for the Chiefs.
But suddenly the game was on.
Worcester grabbed their first try when scrum-half Jonny Arr fed Pennell to score. Then wing Lemi kicked upfield from just inside his own half and followed up to beat wing Matt Jess for pace and grab the converted try.
Exeter dented the comeback, though, as Yeandle scored two tries either side of the break, both converted by Steenson, to put his side in command, the first of which also claimed the try bonus point.
But Worcester, to their credit, would not lay down.
Lamb booted a penalty just before Yeandle's second score.
Creevy's 53rd-minute try, that his stand-off converted, plus Lemi's second on the left moments - all after Exeter replacement James Scaysbrook was sin-binned for pulling down a maul on his own line - gave the Warriors a try bonus point.
The momentum had switched and Worcester had Exeter on the rack even when they were back up to a full complement of players.
And, after Lamb's third penalty put Worcester within five points, the match came down to one cross kick by the fly-half which wing Josh Drauniniu failed to grab with the line at his mercy to finish a great game.