With less than two minutes of the game remaining they trailed 26-19 before tries from Phil Dollman and Sireli Naqelevuki and a conversion from Gareth Steenson broke the Warriors' hearts.
Exeter also overcame the loss of two players to the sin-bin in the second half with wing Gonzalo Camacho fortunate to escape with a yellow card for a dangerous tip tackle.
Worcester began strongly and should have taken an early lead.
The Warriors won a lineout in the visitors' 22, Marcel Garvey headed for the line to make the extra man and slick transfers gave Chris Pennell a great opportunity for the first try - but the full-back elected to go alone and was held up by some desperate Exeter defence.
The Chiefs soon made Worcester pay for that error by taking a ninth minute lead with a penalty from Ignacio Mieres after Exeter produced a formidable line-out drive.
Moments later Pennell was penalised for not releasing but this time Mieres was narrowly wide with his kick from halfway.
Exeter scored the first try of the game after 16 minutes.
At a scrum in the home 22 their pack pushed Worcester off their own ball and they capitalised when a clever crossfield kick from Mieres was collected by Luke Arscott to score the try which Mieres failed to
Back came Worcester with their first score when Craig Gillies was driven over from a lineout close to the Chiefs' line with Andy Goode's excellent conversion reducing the lead to only one point.
An illegal high tackle from James Percival gave Mieres an easy three points but Worcester took the lead with a fortuitous try.
From a ruck near halfway Goode chipped over the home defence, Alex Grove hacked the ball on as did Miles Benjamin but the wing was then fortunate. His overhit effort was clearly destined for the dead ball area but it cannoned off the crossbar and deflected to allow Benjamin to just secure the touchdown with Goode converted.
Goode then missed a 35-metre penalty attempt before Bryan Rennie waltzed past some poor defence from Worcester on the stroke of half-time for a splendid individual try which gave Exeter a 16-14 interval lead.
Within minutes of the restart Mieres had extended the advantage with his third penalty but the Warriors were unlucky not to nullify this as Goode's 45-metre penalty hit a post.
Exeter were dealt a double blow when firstly Camacho was yellow carded for his tip tackle, with Goode kicking the resulting penalty - and then almost immediately Arscott followed his team-mate to the sin-bin for a deliberate offside.
With 20 minutes to go, a 55-metre penalty from Goode gave his side a 20-19 lead before a close call from referee Dean Richards ruled out a try for Garvey. The wing had burst on to a pass from Goode to race past
Mieres and over the line but the wing was recalled as the pass was adjudged to be forward.
Camacho returned in time for Goode's third successful penalty but with Arscott's re-entry the Warriors had not really capitalised on the absence of the two Exeter miscreants.
However Worcester were given a further boost when Goode kicked another goal to give the Warriors some breathing space but that late drama from the Chiefs made sure Worcester regretted their failure to take advantage of Exeter's ill-discipline.
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