Washington trailed 2-0 early -- Tlusty alone outscored the Capitals 3-2 before the second period was 2 minutes old -- but needed just 11 shots over the first two periods to score all five goals.
"When you play with confidence, every chance, whether you're going to score or not, is going to be a hard time for them," Ovechkin said.
In leapfrogging Carolina for second place in the Southeast Division, the Capitals won their seventh in 11 games and won for the first time since 2007 when allowing a hat trick to an opposing player, according to STATS LLC.
"We knew where we were and where we stand, and what games are most important here," Green said, "and tonight was the biggest one for us yet."
They've plunged from the division lead during an injury-riddled stretch in which they have dropped nine of 10, and for the first time since moving from Hartford in 1997, they lost a game when one of their players scored three goals.
"You're still in there. We have to just stay focused," Tlusty said. "Focus is going to be a big key. We still have plenty of games left and we still have a big chance. We played a solid game tonight. It just didn't end up with the W."
Carolina's Dan Ellis stopped four of the seven shots he faced but left after Green's second goal tied it at 3 with 15:34 left in the second. He was replaced by Justin Peters, who stopped nine of 11 shots.
"We sensed their goalie was a little bit hesitant," Green said, "so we threw everything at him."
Ovechkin gave the Capitals the lead for good with 8:54 left in the second when a poor clearing pass led to a 2-on-1 rush that he capped with a goal that made it 4-3 and a celebratory leap into the boards.
Ward then stretched the lead to 5-3 with a short-handed goal with 44.9 seconds left in the second.
"I think we outplayed them, but we gave up too many odd-man rushes, and they always score on them," Tlusty said.
Tlusty scored twice for a Carolina power-play unit that entered as the NHL's worst and was a big reason why the Hurricanes picked up power-play specialist Marc-Andre Bergeron earlier in the day in a trade with Tampa Bay.
That defensive depth may be tested after Pitkanen was hurt with 1:57 left in the second. He was racing to beat an icing call when he went into the boards and was taken off the ice on a stretcher.
Coach Kirk Muller didn't know the extent of the injury and said he thought it was either an ankle or a heel.
Tlusty took care of his hat trick just 1:52 into the second period and just 70 seconds after Green tied it at 2, taking a pretty cross-ice pass from Staal and pushing it past Holtby.
"I was just in the right spot in the right time, and he made a pass right on my stick," Tlusty said.
Tlusty put the Hurricanes up 1-0 midway through the first by stuffing in a rebound, then made it 2-0 roughly 2½ minutes later on the power play with a wrist shot from the circle.
But ultimately, he became the answer to a trivia question: He's the club's first player to record a hat trick in a loss since Jeff O'Neill did it for the Hartford Whalers on Jan. 31, 1997, in a loss to Anaheim, according to STATS.
The Capitals needed just 81 seconds to wipe out that two-goal deficit.
Ovechkin started the rally by beating Ellis with a rising slap shot with 39 seconds left in the first period, and Green made it 2-all with a power-play goal just 42 seconds into the second.
"Green's goal right away in the second was huge," Ovechkin said, "and we just kept going."
Ovechkin extended his points streak to nine games. ... Washington C Marcus Johansson had two assists. ... Carolina D Jamie McBain was a healthy scratch. ... The Hurricanes were busy before the game, activating D Bobby Sanguinetti from injured reserve in addition to picking up Bergeron. ... Washington activated D John Erskine from injured reserve and had him in the lineup.