The victory means Rob Baxter's men will play in Europe's leading club competition for the first time in their history, just two years after winning promotion from the Championship and making their debut in the Amlin Challenge Cup.
Exeter came within a whisker of reaching the semi-finals of the Amlin earlier this month before slipping to a heartbreaking defeat at French giants Stade Francais in Paris and club captain Tommy Hayes admits tasting Heineken Cup rugby will be truly special experience for everyone at Sandy Park.
"Right now we are playing at a level of rugby that an awful lot of people would love to play at and haven't had the opportunity to play in," Hayes told the Exeter website.
"We have that opportunity and we are privileged to be here. That said, we deserve to be here, so we are going to make the most of it.
"Worcester was one hell of a game and it's a brilliant feeling, but there is still something there for us to build on. We're happy with the momentum we've created, but we won't get too carried away.
"We lost a game in the last minute in Paris last week and we said we wouldn't get too downbeat about it, but for the same token we can't get too carried away about winning an 80-minute game of rugby in the last minute."
Exeter take on Northampton in Devon on Sunday knowing victory that taking four more match points than the fifth-placed Saints would secure a place in the Premiership play-offs.
But even if the Chiefs fall short in their attempts to make the top four, the excitement of their entry into the Heineken Cup alongside the likes of continental heavyweights Leinster, Leicester, Munster and Toulouse will ensure the 2011/12 season is viewed as an incredible success.
Exeter's 12 Premiership victories already this term ensures they will become the 60th team to play in the Heineken Cup, with Connacht the most recent newcomers to the tournament.
Their remarkable rise will also take the total number of English sides to have appeared in the Heineken Cup to 13, with current Championship outfits Leeds and Bristol and 10 other Premiership clubs having all been involved. Worcester are the only Premiership side not to have played in the competition.