Patrice Bergeron assisted on the first two goals, then left the game in the third period with an unspecified lower body injury. Sturm added an empty-netter with 2:12 left, with an assist from Bochenski, on a turnaround slap shot from centre ice just seconds after Dwayne Roloson left for an extra skater.
Roloson stopped 20 shots for the Oilers.
Bochenski centred the puck to Zdeno Chara, who swatted at it but couldn't get his stick on it. While it bounced around, it went off defenceman Steve Staios' skate and into the net with 4:47 left in the first. A minute later, Bergeron took a shot from close in and it bounced off Roloson's stick to Sturm, who whacked it in.
It was Bergeron's 100th NHL assist.
The Bruins wore No. 9 patches in honour of Hall of Famer John (Chief) Bucyk, who was honoured before the game for 50 years with the team. He was the last Boston captain to skate with the Stanley Cup.
The quest for another is going slowly. The Bruins are stuck at the bottom of the Northeast Division and eight points behind the No. 8 team in the Eastern Conference.
To shake things up, they traded defenceman Brad Stuart and forward Wayne Primeau to the Calgary Flames on Saturday for defenceman Andrew Ference and forward Chuck Kobasew. Ference made his Bruins debut on Tuesday but Kobasew, who played on Boston College's 2001 NCAA championship team, has been sidelined with an elbow injury since late January.
Notes: The Oilers hadn't visited Boston since Nov. 11, 2003. The Bruins haven't lost to Edmonton at home since 1996. ... The Bruins are 3-0 against the Northwest Division. ... Oilers forward Fernando Pisani, who sustained a concussion on Sunday against Atlanta, didn't play.