Two textbook tries in the opening 14 minutes, from Chris Wyles and Chris Ashton, gave the visitors a comfortable lead, but Connacht hit back with tries from Kieran Marmion and Danie Poolman and were level at 17-17 at the break. The only points in the second half came from two Owen Farrell penalties which took the points for the visitors.
Saracens switch from The Sportsground to Wembley Stadium on Friday night for their second round clash with four-time champions Toulouse. It will be the English Premiership club's third Heineken Cup tie at the venue and they will be hoping to break their UK Pool record attendance of 45,892 set when Leinster were the visitors to Wembley in a 25-23 defeat in 2010.
Toulouse warmed-up for their 133rd Heineken Cup outing with a 38-5 home win over Zebre that earned them a bonus point to take the lead in the Pool. But they have lost three of their last four away games in England and a lost their last three away games in all European competitions.
Connacht travel to Zebre, who are still awaiting their first win in Europe. The two teams have already met in the PRO12, with Connacht taking the spoils with a 26-16 home win.