Delighted Exeter coach Rob Baxter celebrated his side's qualification for next season's Heineken Cup after the 31-26 win at Worcester.
The Chiefs trailed 26-19 with less than two minutes remaining before tries from Phil Dollman and Sireli Naqelevuki and a conversion from Gareth Steenson broke the Warriors' hearts.
And Baxter said: "The boys are elated. It's a fantastic achievement to qualify for the Heineken. We also have Northampton at home next Sunday in what is a virtual winner-takes-all game for a Premiership play-off spot."
Baxter accepted his side's good fortune in winning a thrilling match courtesy of their dramatic late rally.
"I thought it was a loss, we weren't quite on our game today but it takes a good side to score four tries against such a tight defence as Worcester's," he said. "We gave away too many penalties."
Worcester coach Richard Hill was downcast after his side's defeat.
"It was a massive blow to us," he said. "It's not very pleasant, we should have kicked long with the final restart to give them more to do.
"We blew a couple of opportunities and should have made more of their two players in the sinbin but I still thought that we were in control of the game."
Worcester still face the lingering threat of relegation but Hill is confident they will remain in the top flight.
"We are still not mathematically safe but it will be difficult for Newcastle to pick up two bonus-point wins against Saracens and Wasps. However, we have to make sure we win at home to London Irish next week."