David Krejci and Reilly Smith, the only two players to beat Howard in 65 minutes dominated by Boston, both scored again in the shootout to give the Bruins a 3-2 victory Wednesday night.
"That was a real tough win, but a win we deserved," Julien said. "It's probably the best game we've played to this point, but Howard played very well."
The Bruins outshot Detroit 35-18 in regulation, and Howard made three key saves in overtime — the last to stop Torey Krug at point-blank range.
"Howie stole a point for us tonight," Detroit coach Mike Babcock said. "Boston competed harder than we did and they played better than we did, so we're happy to get a point out of this."
Howard, though, was beaten on both shootout attempts while neither Gustav Nyquist or Andrej Nestrasil could get their shots on net. Nyquist, who tied the game with a power-play goal at 2:59 of the third, fired over the crossbar, while Tuukka Rask poke-checked the puck away from Nestrasil.
The Bruins, who have only scored six goals in a 2-3-0 start, snapped a three-game losing streak.
"That was a pretty solid 65 minutes to snap the streak," Rask said. "We skated really hard and made some sweet passes, but Jimmy played a great game and kept them in it."
Boston had two great chances in the final minute of regulation, but Howard made a pad save on Dougie Hamilton, then knocked away Simon Gagne's attempt to put in the rebound.
The Bruins got on the scoreboard first, taking advantage of Detroit's neutral-zone turnover. Krejci came in alone against Howard and beat him on the glove side for his first of the season at 5:12 of the opening period.
Tomas Tatar tied it at 8:40, picking up a loose puck at the bottom of the face-off circle and beating Rask for his first of the year.
Rask stopped Luke Glendening on a breakaway early in the second period. Moments later, Howard made a point-blank save against Brad Marchand on a 2-on-1 break.
Smith then gave the Bruins a 2-1 lead with 6:29 left in the period, one-timing a pass from Patrice Bergeron for his second goal.
"That's exactly what we've been working on in practice," said Smith, who was playing against his brother Brendan for the second time in six days. "Get the puck down low and try to get a dirty goal."
Nyquist's tying score was his third goal in three games, including the Red Wings' only two power-play goals.
Nyquist and Johan Franzen picked up back-to-back penalties, but Howard made four saves on the two power plays, making Detroit a perfect 10 for 10 on the penalty kill this season.
Daniel Paille hit the post moments after Boston's second power play, but the lethargic Red Wings struggled to take advantage.
"I looked up at one point in the first period, and they had won 11 faceoffs and we had won two," Babcock said. "When that happens, you are always chasing the puck, and it didn't get any better all night."
NOTES: Bruins assistant coach Doug Houda needed multiple stitches in the top of his head after being hit by a puck during the second period. Houda was joking and fist-bumping players as he walked to the dressing room, and was back on the bench before the period ended. ... Gagne played his first game since the 2012-13 season, a day after signing a one-year $600,000 contract with the Bruins. ... In a schedule oddity, the Red Wings were hosting the Bruins for the second time in their first three games of the season.