Neil tied it at 2 at 8:57 when his centering pass went in off Montreal defenseman Jeff Woywitka. Milan Michalek scored late in the second as the Senators overcame a 2-0 deficit to split back-to-back preseason games between the teams.
"I always like getting booed in another team's building," Neil said. "Usually it's for a fight or something so whenever you get a couple of goals it's always nice."
Michael Cammalleri scored two goals 2:39 apart in the second period for the Canadiens, who erased a three-goal deficit in a 4-3 shootout win Friday at Ottawa.
Robin Lehner stopped 22 shots for the Senators (2-1-1).
Carey Price made 25 saves. He has allowed 10 goals in just over 120 minutes through three starts.
"It's a process," Price said. "Now is the time to work on things, little details that will make a difference when it comes to the real deal."