Mason stopped 19 shots for his 19th career shutout, and Oshie scored 26 seconds into the third period in St. Louis' 1-0 victory over Minnesota on Thursday.
Oshie, a former Minnesota high school star, fired a wrist shot from the top of the left faceoff circle past goalie Josh Harding for his ninth goal of the season.
St. Louis won consecutive home games in regulation for the first time this season. The Blues (20-19-7) also tied a season high with their third win in a row.
Minnesota (24-21-3) had its four-game winning streak snapped.
Oshie, who broke a 10-game scoreless string in a 4-3 win over the Kings two games ago, had his third game-winning goal of the season.
"I was just trying to put it on net and it went in," Oshie said. "We shot often and early. We kept going and eventually it's going to do in."
Harding didn't get a good look at the puck, which deflected off defenseman Kim Johnsson. "As a goaltender, your job is to keep the other team out," Harding said. "At the [beginning] of the period, you've just got to be ready."
Mason posted his first shutout of the season and his first since April 12, 2009. He stopped Eric Belanger from close range midway through the third period. He also got plenty of help from his teammates, who blocked 13 shots.
"A shutout, it goes on my stats, but it's definitely a team statistic in my opinion," Mason said. "The guys did a great job. I wouldn't have gotten this without the great play of our team."
St. Louis defenseman Mike Weaver blocked a game-high six shots including two in the third period.
"To me, those were definitely Grade A scoring chances," St. Louis coach Davis Payne said of Weaver's key stops. "He handled it perfectly."
The Blues had 18 shots on goal in the first period, tying a season best set in the second period of 3-1 win at Nashville on Nov. 27. They had 37 shots overall.
St. Louis improved to 8-14-3 on home ice, still last in the league with 19 points. But Oshie feels the back-to-back home triumphs are a sign of better times.
"It was good to get a couple for the fans," he said. "It's a good feeling in the locker room, getting a couple wins and stringing a couple together."
Minnesota dropped to 5-5 on the back end of back-to-back games. The Wild beat Vancouver 5-2 on Wednesday.
"We battled, we competed," Wild coach Todd Richards said. "I think we helped their cause a little bit -- too many turnovers."
- The Blues released goaltending consultant Ed Belfour on Thursday. "He was a part-time guy and he was great for us," said team president John Davidson. "He made a decision that his family is first."
- Wild goalie Niklas Backstrom was given the day off after recording his franchise-record 114th victory Wednesday night in a 5-2 win over Vancouver.
- St. Louis defenseman Erik Johnson has failed to record a point in his last five games.