Matt Carle and Mike Grier also had goals, and Joe Thornton added three assists as San Jose snapped the Penguins' five-game winning streak and ended Pittsburgh's stretch of four straight road victories to start the season.
Michel Ouellet and Dominic Moore scored for Pittsburgh.
The Sharks overcame the ejection of right winger Jonathan Cheechoo just 1:03 into the penalty-filled game that was uncommonly testy considering the teams rarely play each other.
Malkin, the rookie of the month for October who had scored at least once in each of his first six NHL games, was trying to become the first player to score in the first seven games of his career. Nobody has accomplished the feat in seven games to start a season since 1992-93, when Pittsburgh's Mario Lemieux began with a 12-game streak.
Pittsburgh was on its best winning streak since getting six straight victories from Jan. 17-26, 2002, but the Penguins have had trouble in recent years on the road against the Sharks. They are 0-6-1 in San Jose since a win on Oct. 22, 1997.
This was the third game of a four-game trip that had a stop in Los Angeles and concludes Monday at Anaheim.
There were 15 penalties, 10 in the first period when the teams briefly played 3-on-3. Each team had a goal waved off, too, because of infractions that happened before the puck found the net. The sellout crowd of 17,496 booed loudly when the buzzer finally sounded to end the long opening period, then again when the officials skated out before the second.
McLaren - whose earlier goal was disallowed - made his second opportunity count, scoring on the rebound one minute into the second. He passed to Joe Thornton, who fired a shot that rebounded off Marc-Andre Fleury's chest. McLaren charged in and backhanded in a chip shot while using only one arm, marking the first time in his career he's scored in consecutive games.
Ouellet tied it at 7:20 on a 2-on-1 breakaway, beating goalie Vesa Toskala stick side in the lower left corner for his fifth goal. San Jose took a 2-1 lead on Carle's power-play goal at 9:44.
Moore, who also had an earlier goal waved off, scored 1:45 into the third period for Pittsburgh.
Toskala made 25 saves for the Sharks, who had lost the last two on home ice including a 3-1 defeat to the New York Rangers on Thursday.
For fans at the Shark Tank, seeing the Penguins was a rare treat and the chance to watch an exciting matchup of two of the NHL's top teams on the power play. The way the non-conference schedule works, Pittsburgh won't come back to San Jose until the 2009-10 season.
Sidney Crosby, Pittsburgh's second-year pro who had a sensational rookie season, took part in the physical play early. He came in with only six minutes in penalties, but took a seat 1:03 into the game for roughing - and Cheechoo was done for the night at the same time.
Cheechoo got a major for boarding and a game misconduct when he landed hard on Mark Eaton after Eaton had slipped. Crosby entered the fray and began punching Cheechoo, leading to his penalty.
Notes: Pittsburgh is 2-2 vs. Western Conference. ... The Sharks are 2-8-1 in their last 11 meetings with the Penguins. ... Fleury finished with 31 saves.