Rust controlled a bouncing puck at the top of the crease and fired it past Joonas Korpisalo for the winner and his 10th goal of the year.
Tristan Jarry stopped 17 shots for his third shutout in his last four appearances. Jarry, who has five career shutouts, and three this season, established a franchise-record 177-minute, 15-second shutout streak before the run ended during Tuesday’s home loss to Montreal.
Korpisalo, who beat Pittsburgh on Nov. 29, made 31 saves. Columbus has lost four of five and six of nine.
Six of the last 14 games between Pittsburgh and Columbus have been decided after regulation.
Blue Jackets forward Pierre-Luc Dubois was whistled for slashing 1:25 into overtime, which led to the winning goal. Pittsburgh’s Kris Letang became the second defenseman in team history to record 200 career power-play points with an assist on the winner.
The Penguins won for the fourth time in five games and the seventh time in 10 contests. Pittsburgh has points in 16 of its last 21 games, which includes 12 wins. The Penguins won their ninth straight home game against Columbus, dating to Dec. 21, 2015. Pittsburgh has 13 wins in its last 15 home games overall.
Star forward Evgeni Malkin didn’t play for Pittsburgh because of an illness. He is one goal from becoming the fourth in franchise history and eighth active in the NHL to score 400 goals. Malkin has six goals and 21 points in his last 14 games.
Captain Sidney Crosby missed his 15th game and Nick Bjugstad his 13th, both because of core muscle surgery in November, and Pittsburgh played Thursday without three of its top four centers. The Penguins have also been without top defenseman Brian Dumoulin and forward Patric Hornqvist, who missed their fifth straight games with lower-body injuries.
Pittsburgh last played without Crosby and Malkin on April 9, 2017, a 3-2 loss at the New York Rangers in the Penguins’ regular-season finale. The Penguins have won 15 of their last 21 in the regular season without Crosby and Malkin, including seven of the last nine at home.
Entering the third period in a scoreless tie, Pittsburgh led Columbus 18-11 in shots.
Jarry made a first-period pad save on Oliver Bjorkstrand on a breakaway. In the second, Penguins defenseman Marcus Pettersson tripped Sonny Milano on another breakaway, resulting in a failed power play. Jarry stopped Dubois on a third-period breakaway.
Pittsburgh’s Teddy Blueger also missed the net on a breakaway in the third.
NOTES: Pittsburgh has points in 11 of its last 12 home games, which includes 10 wins. … The Penguins have 11 wins in their last 15 games against Columbus, dating to Feb. 3, 2017. … Penguins D Jack Johnson played in his 900th NHL game. … D Seth Jones played his 300th game with the Blue Jackets. He is one game from 500 in his NHL career. … Milano is one game from 100 in his NHL career. … Jake Guentzel continued a four-game point streak with an assist. He has points in 11 of his last 13 games overall.
Blue Jackets: Close a four-game trip Saturday at Ottawa
Penguins: Finish a three-game homestand Saturday against Los Angeles.