Guentzel tied it 2-2 at 7:04 of the second period, swatting a shot five-hole on Merzlikins while falling to his knees in the slot.
Karlsson gave the Penguins a 3-2 lead at 8:40 of the third period with a one-timer from the top of the left circle off a cross-ice pass by Evgeni Malkin. Karlsson has 11 points (four goals, seven assists) during a six-game point streak.
Alexandre Texier tied it 3-3 at 11:45 when he buried a rebound past a lunging Jarry near the left post.
"System-wise I think we were pretty good," Blue Jackets coach Pascal Vincent said. "Managing the puck became an issue at some point, and the battles, 1-on-1s. So, the compete level, it's not the systems ... no systems are perfect, but the compete level at key times wasn't good enough."
NOTES: Crosby's hat trick was his 13th in the NHL. ... Guentzel has nine points (four goals, five assists) during a five-game point streak. … Columbus was 1-for-1 on the penalty kill and is 22-for-22 in its past nine games. ... Werenski had the secondary assist on Chinakhov's goal. It was his 174th in the NHL, moving him past Seth Jones for the most by a defenseman in Blue Jackets history.