St. Louis won its third straight game after trailing in each. Ottawa led 2-0 in the first period and 3-2 entering the third.
"I think that we're just confident. We know that we're going to have a chance," Blues center Ryan O'Reilly said. "Our goaltending has been outstanding; we know that they're going to shut the door. And for us, when we get to our game, we know we're going to get opportunities, and we've done a good job at capitalizing on them at the right times."
[WATCH: All Blues vs. Senators highlights]
Perron scored his 200th and 201st NHL goals, O'Reilly had a goal and three assists, and Jake Allen made 25 saves for the Blues (3-0-1).
"I heard about [the milestone] last game when I scored the other one," Perron said. "It's definitely nice to hit that one. As you get older, there are different things like that that happen, it's pretty cool."
Vitaly Abramov scored his first NHL goal, and Anders Nilsson made 31 saves for the Senators, who are off to their worst start (0-3-0).
Video: STL@OTT: Abramov taps home puck for first NHL goal
"I thought we could've won the game," Senators coach D.J. Smith said. "We had some long stretches where they were in our zone, but I thought we boxed out hard, we battled hard in our zone, especially early. I think they just wore on us as the game went on."
Perron's snap shot bounced off Anders Nilsson's left pad and into the top right corner to make it 5-4.
"I practice a lot," Perron said when asked whether his shot has improved. "I've done a lot of things that last couple years. I've changed my stick, did some things, really focused on what some of the guys are doing to score goals in this league. You see a guy like Auston Matthews, Patrik Laine, the young guys came in the League and they're really shooting the puck, and that caught my attention. I changed some things on my part, and I feel like my shot's been better since then."
Video: STL@OTT: Perron wires home wrister for PPG
Abramov gave the Senators a 1-0 lead at 8:10 of the first period when he shot into an open net after Allen misplayed a dump-in behind the net.
Artem Anisimov one-timed a pass from Connor Brown at the top of the slot to make it 2-0 with 53 seconds remaining. It was his first goal with Ottawa.
Perron cut it to 2-1 with a wrist shot on the power play at 9:07 of the second.
Oskar Sundqvist picked up a loose puck following a face-off in the offensive zone and made it 2-2 at 11:32.
Chris Tierney scored shorthanded on a breakaway to give Ottawa a 3-2 lead with 2:11 left in the second.
Jay Bouwmeester's one-timer from the point got through traffic in front and went under Nilsson to tie it 3-3 at 1:38 of the third.
Brayden Schenn gave St. Louis a 4-3 lead on a 2-on-1 at 12:47.
Video: STL@OTT: Schenn nets goal following turnover
"[The Blues are] a very good team that rolls four lines over, so you've got to be prepared," Smith said. "They have maybe the best defense in the National Hockey League. We found ways to get scoring chances, but we made some mistakes that ended up in our net."
Anthony Duclair beat Allen with a wrist shot to tie it 4-4 at 14:12.
O'Reilly scored into an empty net with 1:16 remaining for the 6-4 final.
"Obviously, with winning a [Stanley] Cup (last season), I think [we're] much more confident," O'Reilly said. "Having been through that as a group, I think we just seem to get more bounces. Last year, at the beginning of the year, every bounce that could go wrong did. We couldn't find a way to close games out. But it's a different year, and we've improved."
They said it
"Definitely not as smooth as I usually am, but it's coming. It's been the first real meaningful game in six or seven months, so for me, it was just good to get the feet wet. I felt that I made some really good saves. There are some things to adjust, but overall, we'll take the win." -- Blues goalie Jake Allen on his season debut
"I thought he skated well. He put pucks in, he went and got them, he got rewarded, he scores in front of the net. Probably looking back, [I'd] get him a few more minutes, but I thought the kid was really good." -- Senators coach D.J. Smith on Abramov, who played 8:27 in his season debut and second NHL game
Need to know
Allen tied Curtis Joseph for second on the Blues wins list (137). … It was O'Reilly's second four-point game in the NHL. He had two goals and two assists for the Buffalo Sabres in a 6-2 win at the Edmonton Oilers on Oct. 16, 2016. … With an assist on Anisimov's goal, Senators forward Vladislav Namestnikov got his first point since being acquired in a trade with the New York Rangers on Monday. … Ottawa defenseman Erik Brannstrom got his first NHL point with an assist on Duclair's goal.
Blues: At the Montreal Canadiens on Saturday. (7 p.m. ET; NHLN, CITY, TVAS, FS-MW, NHL.TV)
Senators: Host the Tampa Bay Lightning on Saturday. (4 p.m. ET; TVAS2, TSN5, SUN, NHL.TV)
Video: Perron, Blues power past Senators, 6-4