Weiss, who has two goals this season, broke a 1-1 tie with a wrist shot past Boston goalie Tuukka Rask 8:21 into the second period. Cleary came through with his first goal of the season on a quick blast past Rask at the 10:41 mark.
The goals by Weiss and Cleary came while Detroit goaltender Jonas Gustavsson was stopping 11 shots in the second period. Gustavsson was a late substitute for Jimmy Howard, who missed the game because of a hand injury. Gustavsson had 29 saves overall.
Milan Lucic score with 1:20 left in regular to pull the Bruins within one goal. It was his third goal of the season.