Auld, acquired from Phoenix on Dec. 6 after starting goalie Tim Thomas went down with a strained groin, improved to 4-1 with Boston. It was his fourth career shutout and second this season.
Before being dealt to Boston, Auld had been sent by the Coyotes to San Antonio of the AHL on Nov. 20.
"Tim carried the load for us most of the year and Alex has stepped in and done a good job," Boston coach Claude Julien said. "Our goaltending is one of the reasons we are where we are right now."
After the game, the Bruins activated Thomas from the injured list and sent backup Tuuka Rask to Providence of the AHL.
Auld knew the trade was timely for him and the Bruins.
"It's been great," he said. "Coming here was awesome, and having a chance to play a lot has been great. Being able to work through some things after not playing for a while, I think any goaltender will tell you playing a lot will help."
The Bruins remained the only team not lose consecutive regulation games despite getting only 18 shots. They fell 3-1 to New Jersey on Thursday.
"We want to be a team that creates chances," Bruins defenseman Zdeno Chara said. "But at the same time we don't want to play the open, up-and-down game. We want to play well defensively."
Marco Sturm added an empty-net goal with 11.9 seconds left to ruin the Blue Jackets' first visit to Boston since Jan. 18, 2003.
Boston, which entered with the NHL's worst penalty-killing percentage, held Columbus scoreless in five chances, including one in the closing 2½ minutes.
"They play a system that can be frustrating for you," Blue Jackets defenseman Adam Foote said. "They have the five back and they give you the outside and it looks like you have a good opportunity and they take it away. Auld stayed strong on the first shot and we just have to get in on those rebounds."
Reich scored 3:20 in when he redirected Petteri Nokelainen's short pass behind goalie Fredrik Norrena. Reich started the play with a slap shot from the left wing and hustled into the slot when the puck bounced off the backboards to Nokelainen.
Auld stopped Rick Nash on a clean breakaway in the closing minute of the second period. With the Blue Jackets playing short-handed, Nash intercepted a pass at center ice, but Auld made a left-pad stop.
"I think the puck rolled a little and rolled off my stick," Nash said.
Bruins defenseman Aaron Ward stopped Nash's chance to move in alone again by making a diving stick check.
Nikolai Zherdev had the best chance before Nash, taking the puck from his own blue line and shifting around Chara before firing a wrist shot from the right circle that Auld handled.
- Auld's other shutout this season was a 1-0 win for Phoenix at Anaheim on Oct. 25.
- This was the only meeting between the teams this season.
- Columbus RW Jared Boll, who entered as one of three NHL players with over 100 penalty minutes, received a fighting major 2:18 in.
- The Bruins played the second of five straight home games. They host Northeast division-leading Ottawa on Tuesday.
- Boston scored first for the 16th time in 24 games, winning its 11th.