Ulster captain Andrew Trimble was relieved to end up with the win after a "proper old school dog fight" with Exeter at the Kingspan Stadium.
Paddy's Jackson's drop goal two minutes from full-time gave the Irish province a dramatic 19-18 victory that keeps alive their hopes of progressing in the Champions Cup.
Exeter had looked set to take the spoils themselves and bounce back from last week's 35-8 home defeat to Clermont Auvergne when Gareth Steenson put them ahead with a 76th-minute drop goal.
However, Jackson responded to put Ulster back in front and that proved enough to secure victory as Steenson missed with another drop goal attempt right at the end in a thrilling finale.
Trimble said after his side moved onto four points in Pool Five with the win : " It was one of those finishes to a game that was entertaining and I think a lot of supporters got their money's worth, but it was a little bit too entertaining at the end, we had to dig really deep.
"That is an Exeter side that is hurting a bit from last week's result and they came out fighting. The first 15-20 minutes when it was dry we were able to take them through phases and move them about the pitch and keep the tempo up, then it just became a proper old school dog fight out there.
"Whenever it comes down to that it's about who wants it more and who has more character and who is going to be brave enough to stand up and take the game by the scruff of neck, and we had to do that a couple of times.
"Whenever there is three or four minutes left and you have to get down there we put Jackie in the pocket and he delivered.
"I am very proud of the performance and there are definitely things to work on."
Exeter prop up Pool Five and are now nine points adrift of leaders Clermont, but coach Rob Baxter is not giving up hope of making the quarter-finals and is drawing on inspiration from last year, when the Chiefs finished top of their pool despite losing three times.
"We topped the pool last year that was won by a team with 16 points and there are four games left and we have a point. We'll keep fighting to the death and the one thing we have learned if you fight to the death you always have an opportunity," said Baxter.
"We'll keep going for it, wrapping up tonight the players are hurting for the right reasons. Last week they were hurting for the wrong reasons because we didn't give ourselves a chance to get into that game and tonight we did.
"To come to Ulster with such a good crowd and atmosphere and to stand and fight and refuse to get bowed, because there were moments when they got some momentum, and refuse to bend and to be within one or two feet of a drop goal going over and us winning what would have been a remarkable game...
"I'm disappointed but for the right reasons and I think we learned a little bit about ourselves tonight."