Vladimir Sobotka won a faceoff in Ottawa's zone and Jeff Lovecchio fed the puck to the point, where Fata drove a slap shot through traffic past Pascal Leclaire.
Brad Marchand scored a power-play goal late in the first period for Boston (5-1-1).
Thomas, last season's Vezina Trophy winner as the NHL's top goalie, won for the second time in two nights.
"Tonight and last night he showed why he's one of the top goalies in the league," Fata said.
Thomas said that he, coach Claude Julien and goaltending coach Bob Essensa made a group decision to start consecutive nights on the road.
"(Essensa) actually kind of likes it when I'm playing a little bit tired because I'm a little bit more controlled," Thomas said. "I think he was thinking it would help me get back into a rhythm that way because the second game I'd be a little bit more conservative."
Thomas led the Bruins to a 2-1 shootout win in Montreal on Thursday that saw him stop each of the Canadiens' three attempts after making 33 saves during the game.
"(Thursday) I felt completely comfortable right from the start," Thomas said. "Today, actually, I didn't feel uncomfortable but I had to work at it a little bit harder, maybe because it's back to back. That's a good learning experience going into the season because there are going to be situations like this and fortunately I was able to get through the little bit of uncomfortable stage at the beginning."
Ryan Shannon scored a power-play goal for Ottawa in the first.
Leclaire stopped 18 shots for the Senators, who finished the preseason 2-4.
"I think he's been outstanding the last few games he's played, he's been real solid," Senators captain Daniel Alfredsson said. "It's confidence. We gave up a few chances off a couple of turnovers where he makes the big save and as we get better and better, we can make it easier for him."
Shannon opened the scoring on a power play 12:43 in. Thomas went down to stop Chris Campoli's shot from the deep slot and made a vain lunge at Shannon's shot off the rebound into the right side which put the Senators up 1-0.
Marchand drew Boston even with a power-play goal with 59.2 seconds left in the first. Positioned in the slot, Marchand deflected Derek Morris' point shot and the puck floated past Leclaire into the right side of the net.
"It was a great tip," Morris said. "If they give you a target, we'd better be able to hit it."
|PPG - Ryan Shannon (1) Wrist shot - ASST: Chris Campoli (1), Jason Spezza (1)|
1 - 0 OTT
|PPG - Brad Marchand (1) Tip-in - ASST: Derek Morris (1), Marc Savard (1)|
1 - 1 Tie
|Drew Fata (1) Slapshot - ASST: Jeff Lovecchio (1), Vladimir Sobotka (1)|
2 - 1 BOS
|Power Play %||30.8%||21.2%|
|% on Road||27.3%||32.0%|
|% at Home||34.4%||14.6%|