Crosby capped a wild finish for the Penguins before a sellout crowd of 20,074 at Scotiabank Place.
Pittsburgh (36-21-9) rallied from a 4-1 third-period deficit to win for the second straight time in a shootout and third time in four games overall.
Rookie Jordan Staal and Ryan Malone each had a goal and an assist for the Penguins as goaltender Marc-Andre Fleury was pulled after giving up three goals on seven shots in the first period.
However, Staal, with his league-leading seventh short-handed goal of the season, Gary Roberts and Malone scored within a 2:48 span of the third.
Erik Christensen beat Senators goaltender Ray Emery in shootout, but Evgeni Malkin was stopped. Fleury’s replacement, Jocelyn Thibault, stopped Dany Heatley and Antoine Vermette before giving up a goal to Dean McAmmond. Crosby’s goal decided things.
Mike Fisher, Christoph Schubert, Chris Kelly and Heatley scored in regulation for the Senators (38-23-6), who blew a 3-1 third-period lead in a 4-3 shootout loss Sunday at Chicago.
After Colby Armstrong put the Penguins ahead less than six minutes into the game, Fisher, with a power-play marker, and Schubert replied within a 1:55 span.
Kelly then added a short-handed goal as the Senators chased Fleury.
Heatley then extended his point-scoring streak to 12 games with a power-play goal early in the second. He has 10 goals and nine assists during his run.
Senators centre Jason Spezza, who was also riding an 11-game point streak (seven goals, 12 assists) before the contest, was a last-minute scratch with a back injury.
The victory brought the Penguins to within a point of the Senators for fourth in the Eastern Conference standings, with Pittsburgh having a game in hand.
Emery made 23 saves for the Senators, who had beaten the Penguins in seven straight games and were unbeaten in eight meetings between the teams.
Thibault made 15 saves the rest of the way for Pittsburgh.
Crosby, the NHL scoring leader, was held off the scoresheet in regulation for the fourth time in five games but, just like he did against the Flyers, he scored the clincher in shootout to earn his team the win.
With just one goal in eight games and two in 17 heading into the game, Crosby appeared frustrated, taking a couple of minor penalties and getting involved in an exchange with Senators captain Daniel Alfredsson from the penalty box.
Crosby has just two assists in five career games against Ottawa, which went 2-for-9 on the power play.
Pittsburgh, meanwhile, finished 0-for-4.
The Penguins took the lead at 5:56 of the first when Armstrong’s pass attempt from behind the net hit Emery’s pads and went in.
Fisher scored on a rebound to tie the game midway through the first before Fleury was guilty of giving up a couple of suspect goals to Schubert and Kelly, respectively.
Fleury looked particularly bad on Kelly’s slapshot from the blue-line, which hit the netminder and slipped through his pads.
Thibault was in goal to start the second and didn’t look much better in allowing a sharp-angled shot by Heatley to trickle through his pads during an Ottawa power play.
Staal fired a wrist shot over Emery’s shoulder at 9:22 of the third for his 27th goal of the year and Roberts made it 4-3 at 11:02. By the 12:10 mark, Malone had tied the game with another wrist shot over Emery’s shoulder.
Notes: Left-winger Peter Schaefer shook off a shoulder injury to play his 300th game in a Senators uniform . . . Ottawa begins a home-and-home series with the Toronto Maple Leafs on Thursday at Scotiabank Place. The rubber match at Air Canada Centre is Saturday . . . Pittsburgh is home to the New Jersey Devils on Thursday.