The Sabres scored four unanswered goals in the third period.
They now have split the first four games of a team-record six-game road trip that concludes Sunday at Colorado.
Buffalo had trouble against Anaheim's Jean-Sebastien Giguere in the first two periods, but beat him at will in the third, scoring four goals in a span of 13 minutes.
Briere had assists on two of the tallies, and has six in eight games this season.
Adam Mair and J.P. Dumont scored in the final eight minutes as the Sabres extended their unbeaten streak against the Ducks to eight games (6