Washington trailed 2-0 early before scoring five goals on its first 11 shots, won its 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.
It also was the Hurricanes' first loss when a player scored three goals since the move from Hartford in 1997.
Carolina's Dan Ellis stopped four of the seven shots he faced.
He left after Green's second goal tied it at 3 with 15:34 left in the second and was replaced by Justin Peters, who stopped nine of 11 shots.
Ovechkin gave the Capitals their first lead 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.
That ruined the first career hat trick for Tlusty, who 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.
Tlusty took care of the 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.
He put the Hurricanes up 1-0 midway through the first by stuffing in a rebound, then made it 2-0 roughly 2 1/2 minutes later on the power play with a wrist shot from the circle.
But ultimately, Tlusty 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.
NOTES: 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.
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