The Lightning also would love to avenge their most lopsided loss of the season as the Bruins continue their five-game road trip in Tampa.
Boston (19-11-4) opened its trip by pulling even with Montreal in the Northeast Division thanks to a 3-2 shootout win over Florida on Monday night -- its second straight victory after a 1-3-1 stretch.
Meanwhile, a 6-0-2 surge has helped the Lightning (21-10-5) tie Washington for the Southeast lead. The Capitals and Canadiens also square off Tuesday, but Tampa Bay coach Guy Boucher insists he's not worried about the standings yet.
"We didn't talk about first place and we won't talk about it," Boucher said. "I rarely talk about standings through the year. I really believe in the process."
That process has sparked a rapid turnaround, with Tampa Bay's rise coming two seasons after the team's second straight last-place finish.
The return of Vincent Lecavalier has certainly helped lately. The four-time All-Star has three goals in his last two games -- including the overtime winner in Sunday's 3-2 victory over Atlanta -- as the captain rounds back into form following a 15-game absence due to a broken hand.
Steven Stamkos and Martin St. Louis continue to lead the way. Stamkos joined Pittsburgh's Sidney Crosby as the NHL's only 50-point scorers with a goal and an assist against the Thrashers, while St. Louis is close behind at 47 -- including 10 in his last five games.
That production has helped the Lightning win six of seven, but Tampa Bay's last three contests have gone into overtime.
"The last few games, we have been getting some fortunate bounces," Stamkos said. "I thought (Sunday) we came out of the gate and we just let them hang around."
The Lightning didn't hang around during these teams' last meeting, an 8-1 Boston home win Dec. 2 that Tampa Bay goalie Mike Smith called "embarrassing."
With Smith sidelined due to a knee injury, Dan Ellis has started the last four games for the Lightning, going 3-0-1 with a 1.92 goals-against average.
It's unclear who will start in net for Boston, but it may be Tuukka Rask after Tim Thomas stopped 32 shots and all three shootout attempts Monday. Thomas has started on back-to-back nights only once in six opportunities this season.
Rask, who led the NHL with a 1.97 GAA last season, has gone 2-7-1 with a 2.57 GAA in 2010-11, filling a backup role due to Thomas' stellar play.
The 23-year-old Finn is 0-4-0 with a 3.34 GAA on the road, including a 3-1 loss at the St. Pete Times Forum on Nov. 22.
Boston has provided little offense for Rask, scoring more than two goals only twice in his nine starts. David Krejci would like to change that trend after scoring two goals Monday, centering a recently reunited line with Michael Ryder and Blake Wheeler, who scored the lone shootout goal.
"Our goal is to have a really successful road trip and you can't do that without a good first game," Wheeler said. "I think we were a little sluggish in the first period, but that was to be expected coming off Christmas season. Everyone recovered well and it's great to get those two points."
Krejci had two goals and an assist and Wheeler added a goal in the rout of Tampa Bay earlier this month.
AccuScore has powered more than 10,000 simulations for every NHL game on ESPN.com, calculating how each team's performance changes in response to game conditions and opponent's abilities. Each game is simulated and the game is replayed a minimum of 10,000 times to generate forecasted winning percentages.