Jonathan Toews and rookie Brandon Pirri also scored for the Blackhawks, who rebounded with a tidy defensive effort following a 7-2 loss in Nashville on Saturday, their most lopsided this season.
Joe Pavelski connected for San Jose in a matchup of two of the Western Conference's top teams.
Versteeg scored his first goal with the Blackhawks since being reacquired in trade from Florida on Thursday. He was a member of Chicago's 2010 Stanley Cup-winning team.
Chicago's Corey Crawford and San Jose's Antti Niemi, the goalies who backstopped the Blackhawks to their two recent Stanley Cup titles, opposed each other.
Crawford, in nets for Chicago's Cup run last season, stopped 23 shots and wasn't heavily tested.
Niemi, who helped lead the 2010 Blackhawks to the championship, stopped 22 as he faced his former team for the 12th time.
Niemi is 5-6-1 against the Blackhawks. He signed with San Jose just three months after winning the Cup with Chicago.
Pirri, who led the AHL in points last year with 75 points, has goals in three straight games and four in his past six.
He scored the only goal of a crisply played first with 3:26 left in the period.
Patrick Kane went down the right wing into the San Jose zone, backing in Sharks defenseman Scott Hannan to the circle. Kane's shot deflected off Hannan and across the crease to the left side of the net, where Pirri buried the loose puck.
Pavelski tied it at 8:16 of the second on a 30-foot shot from the slot that Crawford caught, but then misplayed.
Crawford picked Pavelski's shot out of the air with his glove, but when he lowered it to his side, the puck rolled out and trickled across the goal line.
Sharp put Chicago back ahead at 2-1 just under 4 minutes later on a one-time shot from the left circle. He ripped the puck past Niemi after taking a pinpoint cross-ice feed from Marcus Kruger.
Toews extended it to 3-1 at 3:39 of the third with his team-leading 10th goal by converting a rebound of his own shot.
Niemi stopped Toews' first attempt after the Chicago captain skated out of the right corner, but the rebound dropped inches from the goal line. Toews skated around a scrum at the edge of the crease and tucked in the loose puck.
With Niemi down on the ice and out of the net, Versteeg converted a rebound of Brandon's Saad shot with 4:50 left in the third to make it 4-1.
Sharp was awarded the penalty shot with 1:11 left after being pulled down by Marc-Edouard Vlasic on a breakaway. He fired high over Niemi to connect on the attempt.
NOTES: The Blackhawks placed G Nikolai Khabibulin on injured reserve with a lower-body injury suffered in Saturday's 7-2 loss in Nashville. Chicago called up rookie Antti Raanta from Rockford of the AHL to back up Crawford. Raanta was signed as a free agent from Finland last summer and was 7-5-0 with a 2.83 goals-against average in 14 games with Rockford. ... Chicago RW Marian Hossa missed his second game with a lower-body injury. Coach Joel Quenneville hopes Hossa will be able to play Tuesday in Colorado when the Blackhawks begin a seven-game road trip. ... The Sharks finished a five-game road trip at 3-1-1.