The Penguins scored the first five goals and moved into a share of the best record in the league with Washington.
Martin scored both his goals on the power play during the game's opening 13 minutes. Crosby also had a power-play goal late in the first to make it a 4-0 contest and added a score midway through the second.
Crosby has 23 goals for the season, having begun the night tied for the league lead with Tampa Bay's Steven Stamkos.
Steve Mason opened in goal for the Blue Jackets and gave up four goals on 12 shots. He was replaced by Mathieu Garon, who coughed up three more goals. Columbus lost its fifth straight.
Marc-Andre Fleury made 22 saves to collect the easy victory.