Letang collected a loose puck in the offensive zone and scored with a snap shot from in front off a give-and-go with Tommy Novak, who had two assists.
Letang also had an assist, Sidney Crosby scored twice, and Bryan Rust had a goal for the Penguins (12-6-5), who have won two straight and extended their point streak to three games (2-0-1). Tristan Jarry made 26 saves.
Sean Monahan, Brendan Gaunce and Zach Werenski each scored for the Blue Jackets (11-9-5), who have lost four in a row (0-1-3). Jet Greaves made 20 saves.
Crosby made it 1-0 at 6:10 of the first period, redirecting a Letang pass at the left post.
Monahan scored his first goal in 10 games to tie it 1-1 at 13:40. Jarry made a save on a Brendan Smith shot and the rebound went off the skate of Penguins defenseman Ryan Graves to Monahan, who lifted it past a sprawling Jarry.
Gaunce put the Blue Jackets ahead 2-1 at 3:51 of the second period with a short-handed goal. Miles Wood got Crosby to go to the ice and skated around him, then fed a backhander to Gaunce during a 2-on-1.
Werenski increased the lead to 3-1 at 19:56, one-timing a shot from the top of the left face-off circle after Charlie Coyle dug the puck out of the left corner.
Rust cut it to 3-2 13 seconds into the third period with a snap shot from the to of the right circle.
Crosby tied it 3-3 a 8:28 when he took a pass off the right wall from Novak and broke in alone before sneaking a shot under Greaves’ right arm.