Stamkos has 15 points in his last eight games, registering seven during the winning streak, while St. Louis has 14 in his last 10.
Stamkos also netted the shootout winner in Sunday's 4-3 victory at Florida.
The first-place Lightning (8-3-0) got regulation goals from Stamkos, St. Louis and defenseman Radko Gudas but blew a 3-1 lead entering the third period.
"We probably have the quietest 8-3 record in the league and we like it that way," Stamkos told the team's official website. "You look at our schedule and we've played some pretty tough teams."
They've won five of six, which includes victories over Los Angeles, Minnesota and Chicago.
Gudas scored at 9:58 in the second Sunday but was handed a game misconduct, 10-minute misconduct and minor for slashing less than three minutes later. The Lightning played the final 32:09 of regulation and overtime short a defenseman.
"We feel pretty fortunate that we came up with two points," coach Jon Cooper said. "We played a pretty solid road game, but it was tough losing Gudas with quite a bit of time left on the clock. We were getting a little tired on the back end, but the boys found a way and that's what they've been doing all year."
The Devils have been finding a way to win lately, going 2-1-1 in their last four games after opening 0-4-3.
First-year Devils winger Jaromir Jagr has six assists in the last four games, with two coming in a come-from-behind 4-3 win at Boston on Saturday.
New Jersey (2-5-4) scored all of its goals on the power play against a Bruins team that allowed three power-play goals in its first nine games. It was the Devils' fifth straight game with a power-play goal after managing one in their first six.
"Well, obviously the power play -- four power-play goals tonight," coach Peter DeBoer said. "... We were going to need something special tonight, whether it was a four-star performance from somebody or our power play to click. We got some of that."
The Devils last scored four or more power-play goals Jan. 22, 2008, when they went 5 for 8 in a 7-3 win at Philadelphia. They scored on the power play in six straight games last season from Feb. 3-12.
The Devils placed goaltender Cory Schneider and defenseman Bryce Salvador on injured reserve Monday. Schneider didn't travel to Boston due to a lower-body injury, while Salvador has a stress fracture in his foot.
The Devils went 1-1-1 last year against the Lightning, who earned a 5-4 shootout win at home in the last meeting March 29.
New Jersey's Martin Brodeur is 6-1-1 in his last eight starts against Tampa Bay.