He had been on the bench the past three games while Sergei Bobrovsky started.
"I felt good," Mason said. "I had about a week's worth of practice to get ready for this game.
"We knew it was going to be a big one with them being the only undefeated team in the NHL. We would have liked to have come in and ended that streak, but that didn't happen."
The Blackhawks dominated territorially and in puck possession through the first two periods, but only managed to get one shot past the Blue Jackets goalie.
Both teams had a handful of scoring chances in the first period. Mason made a point-blank pad save on Marian Hossa with 8:30 left, and Crawford stopped Derick Brassard from the slot two minutes later.
Mason denied Hossa on a breakaway 5:30 into the second after Hossa stole the puck from James Wisniewski at the Columbus blue line.
The Blue Jackets failed to convert several close-in attempts during a power-play late in the second, including when Vinny Prospal's shot hit the crossbar to cap a breakaway.
Shaw finally broke through with 1:27 left in the second from the low edge of the left circle. He took Bryan Bickell's backhanded feed from the back boards and ripped a high one-timed shot that beat Mason high on the stick side.
"He saw me coming," Shaw said. "But I wasn't sure, so I gave him a holler and he put it in a perfect area."
Mason made a point-blank pad save on Patrick Kane midway through the third period after Kane made a spectacular spin move and cut across the crease alone.
NOTES: The Ducks went on to win the Stanley Cup in 2007. ... Blackhawks C Dave Bolland missed the game because of an undisclosed upper-body injury. ... Columbus went 1-5 on its six-game road trip. ..The Blue Jackets placed D Jack Johnson (upper-body), on the injured list on Sunday. C Brandon Dubinsky (lower body) and C Artem Anisimov (upper body) were also out.