"We've worked so hard, the guys have been squeezing the sticks so much, that eventually goals were going to come out," said goaltender Marc Denis.
Playing their first game without Craig, the Lightning spread out the offense. Craig, who had a team-high five goals, sustained a sprained right knee in Thursday's game against Philadelphia and will miss four weeks.
"I don't see who is out," Alexeev said. "I just go out there and perform my best."
"(Craig) had a great start and we're going to miss him," Richards added. "But we also know that during that start, we weren't firing on all cylinders. We have other players to step up. Other players did step up tonight and we've got to fill that role."
Trailing 2-1 early in the second period, Tampa Bay took control on goals by St. Louis and Alexeev.
St. Louis had his second goal of the season on a wraparound, scoring at 3:10. Just 22 seconds later, Alexeev put the Lightning up 3-2, whistling a wrist shot from center point past Olie Kolzig.
After failing on three consecutive power plays midway through the second, Tampa Bay went ahead by two goals at 19:01, when Karlsson tapped in the rebound of Dmitry Afanasenkov's shot.
Bad penalties and costly turnovers thwarted Washington from establishing any offensive momentum in the middle period.
"We had too many turnovers and they're an offensive team with a lot of firepower," Sutherby said. "We turned a few too many pucks over and they were all over our net."
The Lightning took a 1-0 lead 5:51 into the game on a short-handed goal by Lecavalier, who converted a long, lead pass from Nolan Pratt. Semin tied it 48 seconds later bulling through three defenders before pushing the puck into the goal.
At 16:07, Green surprised Tampa Bay goalie Marc Denis with a knuckling drive from the top of the slot, giving the Capitals a 2-1 lead.
Midway through the third period, Alexeev scored his second goal, tipping in Dan Boyle's shot to make it 5-2.
Sutherby struck with 7:22 left, his first goal of the year, but 29 seconds later, Richards beat Washington's Ben Clymer to a loose puck along the boards and restored Tampa Bay's three-goal lead.
Ovechkin converted on a power play at the left post with 3:57 to go.
- C Alexeev has points in five straight games, a career high.
- RW Boyd Gordon and D Bryan Muir were healthy scratches for the Capitals.
- Semin, who has eight goals in seven games, is the quickest Capital to score eight goals in team history.