Andreychuk had two goals, and Boyle scored with 33.6 seconds left in overtime as the Lightning beat the Carolina Hurricanes 5-4 victory on Monday night.
Boyle's goal on his own rebound from in close moved the defending Stanley Cup champion Lightning within eight points of the Southeast Division-leading Hurricanes.
"It went in very, very slowly ... it was slow motion," Boyle said. "I'm pretty excited it went in."
"It was a little shaky," Andreychuk said about the team's confidence heading into the game. "We talked about it. Hopefully that's behind us now."
Andreychuk has four goals in the past eight games after not scoring one in 18 straight games. He has 640 goals during his career, including six this season.
"Obviously I've been frustrated most of the year," Andreychuk said. "I want to continue to try to do what I have to do to make this team win. They're going to need goals from me. I have to contribute. I have to get better."
"We should have picked up the win ... there is no doubt about it," said Carolina goalie Martin Gerber, who made 36 saves. "We lost a point here tonight. Especially in those games against them,
we want to get all the points. We don't want to share anything with them. We've got to do a better job next time."
Andreychuk, on the power play at 13:07, and Taylor's goal 56 seconds later gave Tampa Bay a 4-3 lead in the second. Andreychuk tops the NHL's career list with 274 power-play goals. He also tied Denis Savard for 23rd place all-time with 1,338 points.
Power-play goals by Cullen and Staal helped Carolina manage a 2-all tie despite being outshot 16-7 in the first period. Modin and Andreychuk -- with Tampa Bay shorthanded -- had the Lightning goals.
"Although it's just one point we gained on them, it's better than none or losing one," Boyle said. "Hopefully this a step in the right direction."
Staal, who has five goals during a four-game goal-scoring streak, setup Stillman's goal at 3:58 of the second that put Carolina up 3-2.
"It just seems like we're constantly letting this team back into games when we get maybe an edge or a little bit of momentum," Cole said. "It would have been nice to continue to gain momentum and increase our lead, but that's the way it goes."
The Hurricanes are 1-2-1 against Tampa Bay this season. The teams will meet four more times.
Andreychuk has 91 multigoal and 316 multipoint games. ... Cullen has a goal in three consecutive games. The Hurricanes are 9-0-1 when Cullen scores a goal. ... Lightning D Pavel Kubina returned after missing two games with a strained groin. ... Stillman has one goal and seven assists during a five-game point streak. ... Gerber had a five-game winning streak end. ... Tampa Bay G John Grahame had 26 saves. He had lost his previous four decisions after a team record stretch of nine consecutive wins.