Malkin, the highly touted Russian rookie, scored on a wrist shot midway through the third period to put Pittsburgh ahead 4-2 and become the first player to score in his first three NHL games since Jan Caloun did it for the San Jose Sharks in 1995-96.
The Penguins got two short-handed goals from 18-year-old Jordan Staal, their first-round draft pick in June. Michel Ouellet and Sergei Gonchar scored the first two goals for Pittsburgh, and Marc-Andre Fleury stopped 36 shots.
Gilbert Brule, Fredrik Modin and Nikolai Zherdev scored for Columbus, which lost its third straight and fifth in seven games this season.
Malkin spent much of the evening skating alongside the Sidney Crosby, and that connection paid off with his goal 7:04 into the third period.
With less than 10 seconds left on a power play, Crosby gained the Columbus zone on a four-on-two, drew two Blue Jackets toward him while drifting toward the right dot. He passed to Malkin atop the circle, and the rookie beat goalie Fredrik Norrena low to the far post.
Staal's penalty shot came at 7:49 in unusual fashion. His forehand attempt clanged hard off the left post, prompting referee Marc Joannette to signal there was no goal. Before the puck settled, though, it caromed off Norrena's leg pad and into the net. A replay overturned the initial call, and a goal was awarded.
Gonchar, fresh off his overtime winner Thursday against the New York Islanders, helped the Penguins take a 2-0 lead. His slap shot from the centre point was tipped by Ouellet behind Norrena 2:03 into the game. Gonchar then scored at 7:51, immediately after intercepting a poor clear by Rostislav Klesla above the right circle.
The Blue Jackets picked up their play from there, getting the first period's final 10 shots and pulled within 2-1 on Brule's goal at 17:35. Modin tied the score 7:58 into the second period, tucking Anson Carter's feed from behind the net for a 12-foot shot past Fleury.
Pittsburgh regained the lead on Staal's first goal at 14:43.
Zherdev closed the scoring on a two-man advantage at 15:25 of the third period.
Norrena, a Finn making his NHL debut at age 32 after more than a decade of professional hockey in Europe, stopped 29 shots.
Notes Malkin's father Vladimir, mother Natalia and brother Denis watched him play in the NHL for the first time. When their presence was announced, the crowd of 14,637 responded with a standing ovation. ... ... Blue Jackets centre Sergei Fedorov missed a sixth game to a strained shoulder, but he could return Monday. ... It was the teams' first meeting in Pittsburgh since Dec. 13, 2003.