Saracens edged Glasgow Warriors 28-23 at Vicarage Road on Sunday to complete the opening round of matches in the European Challenge Cup.
In a successful weekend for British sides, Bristol beat Bucuresti 27-3 in Romania and Worcester won 25-7 against Viadana at Sixways on Saturday.
On Friday, Newcastle beat Petrarca 50-5 and the Dragons won 50-3 against French outfit Bayonne.
Bath and Harlequins also won against Montpellier and Connacht respectively.
I don't know if it was complacency - we should have won by a much bigger margin
Bristol coach Richard Hill
Saracens scored a penalty try in each half as they fought back from a 16-3 deficit after the Warriors raced ahead with a try from wing Francisco Leonelli and four kicks from Dan Parks.
Kevin Yates added a second try for Sarries, while the second penalty try gave the home side 23 straight points and the victory.
Glasgow salvaged a losing bonus point with a 73rd-minute touchdown by former rugby league winger Hefin O'Hare.
Bristol coach Richard Hill was disappointed his side were unable to match the 106-3 scoreline racked up by Gloucester against Bucuresti in last season's competition.
"We were up for it, but we were sloppy," said Hill. "Bucuresti were strong, and they make life hard for you.
"We made quite a few changes from last week, and we didn't click.
"We thought we could run the ball and score 12 fantastic tries without doing the hard work, but you can't do that at this level. We went away from our game-plan.
"I don't know if it was complacency - I honestly don't know what the reason was. We should have won by a much bigger margin."