Marc-Andre Fleury stopped 26 shots for Pittsburgh, which won for only the second time in six games. Crosby's goal was his second in 11 games.
Ryan Getzlaf scored his 11th goal for the Ducks, who earned just one point during a four-game East Coast road trip. Viktor Fasth made 24 saves but struggled in the final 20 minutes.
Gibbons took a slick backhand pass from Evgeni Malkin to break a scoreless tie 3:56 into the third. The Penguins needed just 62 seconds to make it 2-0, as Sutter deflected a shot from the point by Olli Maatta.
Anaheim responded immediately when Getzlaf scored his fifth goal in four games.
Crosby pushed Pittsburgh back in front by two, finishing the Penguins' three-goal outburst in a span of 4:04.
BRUINS 4, HURRICANES 1
RALEIGH, N.C. • Reilly Smith and Carl Soderberg had a goal and an assist each in the first period, and Boston topped Carolina.
Johnny Boychuk scored midway through the third period, and Milan Lucic added an empty-net goal for Boston, which has 11 points in its last seven games (5-1-1).
Boston killed four Carolina power plays, including 63 seconds when the Bruins were down two skaters. They haven't allowed a power-play goal in 32 short-handed situations since giving up goals on five consecutive power plays in October.
The Hurricanes played their first game since Oct. 24 with Cam Ward in net. Ward, who missed 10 games because of a leg injury, made 26 saves. He rebounded from a rough start in which he gave up two goals on Boston's first four shots.
Tuukka Rask stopped 23 shots for Boston.
FLAMES 5, JETS 4, SO
WINNIPEG, Manitoba • Sean Monahan scored the winning goal in the eighth round of a shootout and Calgary snapped its six-game losing streak with a victory over Winnipeg.
Jiri Hudler had given Calgary a 4-3 lead with 3:26 remaining in regulation, but the Jets tied it on Bryan Little's with six seconds left.
With Winnipeg goalie Al Montoya on the bench for an extra attacker, the Jets swarmed goalie Reto Berra, and Little put a rebound into an open side of the net.
Montoya made 29 saves. Berra stopped 43 shots, including three in overtime, to help the Flames end their 0-5-1 skid.
Calgary's Michael Cammalleri scored his team-leading ninth goal of the season on the power play and added an assist. T.J. Brodie and Lance Bouma also scored.
Michael Frolik, Olli Jokinen and Dustin Byfuglien had goals for Winnipeg, and defenseman Grant Clitsome and Blake Wheeler both added a pair of assists.