Zach Hyman tied it 2-2 24 seconds later, and Brandon Carlo scored at 17:14 on a slap shot from the right point to give Boston a 3-2 lead.
Ceci scored his first goal with Edmonton at 17:41 for a 5-3 lead.
"It [stinks], especially when you feel like you have a good grasp of the game, and it slips away at the end," Ullmark said. "To be completely honest, today was just one of those days where there were some unlucky bounces. What are you going to do about it? There were some breakdowns, but it's going to happen. It's not the end of the world. It's early in the season. Learn from your mistakes and move on."
NOTES: Draisaitl scored his 210th and 211th NHL goals to pass Paul Coffey (209) for sixth in Oilers history. ... Draisaitl had his seventh game of the season with at least three points. McDavid is the next with four. ... Marchand extended his home point streak to start the season to six games. In the past 24 seasons, three Bruins have had a longer streak: Marchand (10 games in 2019-20), Pastrnak (eight in 2019-20) and Torey Krug (eight in 2018-19). ... Ceci signed with Edmonton as a free agent this offseason. ... The Bruins and Oilers celebrated the life of Colby Cave before the game with his widow, Emily Cave, participating in the ceremonial puck drop, in addition to a video honoring his career. The former NHL forward, who played for the Bruins and Oilers, died April 11, 2020, four days after he had surgery to remove a colloid cyst that was causing pressure on his brain. He was 25. Cave played 67 games from 2017-20, 23 for the Bruins and 44 for the Oilers. He scored nine points (four goals, five assists) in the NHL.