Connacht's man of the match John Muldoon said that beating Harlequins, and ending his side's 14 match losing streak, was like "winning the Heineken Cup."
"We were all down in the dressing room just waiting for someone to deliver the trophy to us. It was a massive win for us and we are delighted we've been able to repay the faith and loyalty of our fans," said Muldoon.
"It has been a very difficult few months for us and them losing 14 games in a row and we wanted to end our first Heineken Cup campaign on a high. We wanted to prove we belong at this level and that we weren't just making up the numbers.
"We were annoyed with ourselves for conceding a try so early in the game and I then gave away another three points with a penalty. We knew how hard it was going to be to score points in those conditions.
"A four point lead at half-time didn't seem enough, but we tackled and tackled and hung on in the end."
Connacht's win not only left Harlequins's hopes of reaching the Heienken Cup quarter-finals hanging by a thread, but also ensured that Ulster will definitely make the last eight for the second season in a row.
They meet ASM Clermont Auvergne in France this weekend and now know that their 19 points will carry them through win, lose or draw. It means Ireland will have three quarter-finalists for the first time in the history of the competition as both unbeaten
Munster and reigning champions Leinster clinched their places last weekend.
Connacht coach Eric Elwood was also delighted at finally "getting the monkey off our backs" in the wake of his side's best performance of the season.
"This win shows we can grind out a victory against one of the better teams around and it means we can enjoy a weekend for once," said Elwood.
"We can take great heart from it and if we can keep the same passion in our game for the rest of the season that will be great. I wanted the players to win the game for themselves, but we have to acknowledge the great support we have had - the crowd were magnificent.
"Our discipline was tremendous and to defend like we did for so long was incredible, even though we gave away a silly try by our standards.
"We have been knocking on the door for the past 13 weeks, so I'm happy to take an ugly win. It was one of those nights when it was a disadvantage having the ball and our defence was magnificent."