After a deflating 5-1 loss at home against Edmonton on Thursday, in which the Stars gave the Oilers nine power plays, Dallas rebounded with a strong defensive effort and allowed only one power play.
"That was the first thing we said in the pregame meeting, stay out of the box," Roy said. "They can't score on the power play if they're not on the power play, so they got one that we did a good job killing, but we also stayed disciplined."
For Cole, it was his first goal with Dallas in his second game with the team since he was acquired in a trade with Montreal last week.
Lehtonen was strong after the Edmonton loss, which was his first game back after missing five because of a groin strain.
"He didn't have to hang on a tightrope and he shouldn't have to," Stars coach Glen Gulutzan said of Lehtonen. "I thought he was solid and gave us a shot to win.
"We didn't take any penalties, we just had one, so we were the Boy Scouts of America today. We did all the little things. It wasn't a pretty game to watch, but at the end of the day, you do enough of those in the right way, you're going to get results and we got it."
The Blues lost for the first time in regulation in their past five road games (3-1-1) and are still 6-3-1 away from home.
"We had too many average performances. What can you say?" St. Louis coach Ken Hitchcock said. "Too many average performances doesn't get it done on the road."
Elliott was making his first start since Feb. 11, a span of eight games, after a 0-4-1 record with a 4.67 goals-against average since the beginning of February.
"I thought he rebounded well there," Blues defenseman Kevin Shattenkirk said of Elliott. "He came back in the second and third and he was the reason why we had a chance to win. I think he did a good job coming off a long break there. He hung with it."
St. Louis appeared to tie the game at 2 at 8:59 of the final period, but it was waved off. After Lehtonen stopped Wade Redden's wrist shot from the left point, the rebound bounced off rookie Adam Cracknell's knee and was then directed into the net with his left skate.
"The league told us that the league ruled on it and they said the goal was conclusive that it wasn't a goal from upstairs," Hitchcock said of the call.
Eriksson got his seventh goal at 10:28 to give Dallas a two-goal edge, firing a wrist shot from low in the left faceoff circle between Elliott's pads after receiving a nice cross-ice pass from Jordie Benn.
"It was a nice pass from Jordie and it was nice to see that go in, and definitely to get the win," said Eriksson who has three goals in the past four games after getting just one in the previous 11. "That was nice."
The Blues pulled Elliott for an extra attacker with 2:56 remaining, but a hooking penalty on Perron with 2:04 left put Dallas back on the power play.
Jagr capitalized with his seventh of the season with 59.3 seconds to go, drilling a one-timer from in front after receiving a nice backhand pass from Roy behind the net.
The Blues jumped on top just 4:20 into the opening period on Perron's seventh goal of the season.
Seconds after a Jamie Benn giveaway in the Dallas zone, David Backes fed a cross-slot pass from the right faceoff circle to Perron, who made a nifty move to his backhand that faked Lehtonen to the ice as he stepped around him and tucked it inside the left post.
And while the Blues controlled play for much of the next 10 minutes, Roussel set up the equalizer at 15:59. His slick backhand pass from the right side of the crease found Cole in front for a one-timer that beat Elliott inside the left post.
Lehtonen kept the game tied with a nice save on T.J. Oshie's wrist shot from the left circle with 2:26 left in the first.
Later on the same shift, an Oshie giveaway led to Roy's third of the year with 1:40 remaining. Roy picked off Oshie's pass inside the St. Louis blue line, worked his way to the left circle and fired a wrist shot that burrowed its way through Elliott's right arm and dropped in for a 2-1 Dallas lead.
"I think Roussel's fight gave us a lift," Roy said. "They have big bodies and were working us down low, but Rous's fight gave us a boost and after that, we got that goal by Cole and we took off after that."
The Blues nearly tied it 2:42 into the second while on the power play, as Perron fired a wrist shot from the high slot that Lehtonen got enough of to deflect it just wide of the left post.
Elliott made a nice stop on Cole's point-blank wrist shot at 7:55 with Dallas on the power play.
Lehtonen then came up big with a nice pad stop at 12:55, denying Cracknell's deflection in front.
Stars rookie D Brenden Dillon was a physical force, delivering a game-high 11 hits while logging 25:03 of ice time, much of it against the Blues' top line. ... Cracknell left the game with 7:12 remaining in the third period after crashing face-first into the boards during a collision with Stars D Jamie Oleksiak. He did not return. ... The Stars honored Blues LW Jamie Langenbrunner, who played in Dallas from 1995-2002 and 2009-10, as part of the club's all-time team. Langenbrunner, who is out for the season with a hip injury, helped Dallas win the 1999 Stanley Cup.