"It's nice just to get the two points," said Sanford, making his first start since Nov. 26. "Never mind the shutout."
Tkachuk's goal, his eighth in nine games, extended his goal streak to five games and gave him 15 points in his last seven games.
"Points don't matter to me," Tkachuk said. "Giving my team a chance to win, that's all that matters to me."
The Blues ended a three-game losing streak with only their third home win of the season and sixth overall.
Mayers scored a shorthanded goal with 5:08 remaining. He put the puck between goalie Marc-Andre Fleury's leg after breaking in alone following a turnover.
Weight finished the scoring with an empty-netter with 50 seconds left.
Pittsburgh was shut out for the third time this season.
Sanford improved to 3-4 this season with his third shutout in 16 career NHL games.
Fleury made 39 saves
"It's always tough to lose a game," Fleury said. "It doesn't matter how many shots you face."
Tkachuk opened the scoring less than a minute into the second period off a feed from Mike Sillinger. The play developed as a three-on-one, with Dennis Wideman trailing after Pittsburgh's Sergei Gonchar fell down at the St. Louis blue line when he overskated Penguins rookie star Sidney Crosby's drop pass.
NHL commissioner Gary Bettman attended the game. Bettman is traveling to the Board of Governors meeting, which begins Wednesday in Scottsdale, Ariz. He said the discussion of the Blues' sale at the Governors meeting would be "only in the briefest of terms ... it's an ongoing process."... Blues goalie Patrick Lalime, who cleared waivers Tuesday, was assigned to AHL Peoria. St. Louis recalled goalie Jason Bacashihua to take his roster spot. ... Pittsburgh owner-player Mario Lemieux missed his fourth straight game with an irregular heartbeat. However, he did resume skating Tuesday in Pittsburgh. ... Former Blues player Eric Boguniecki returned to St. Louis for the first time since being traded last week.