Clowe one-timed a pass from Marc-Edouard Vlasic to the inside corner past Crawford, whose seven-game winning streak ended.
"There were opportunities where we had shots from the point or a 3-on-2 rush and he'd get it stopped," Clowe said. "It seems like the last few games they've tightened the D-zone. It was hard to generate any opportunities."
Antti Niemi stopped 28 shots to beat his former team, the defending Stanley Cup champions, for the second time this season.
"Yeah, it's even better," he said, smiling.
Jordan Hendry scored for the Blackhawks, who lost for the second time in seven games since their previous meeting in San Jose on Nov. 24 -- a 5-2 Sharks victory.
Crawford made 28 saves, but failed to tie a rookie franchise record for consecutive victories.
"You can argue that might have been his best game," Chicago coach Joel Quenneville said. "He's the reason we got a point. You can say two, three saves looked like empty-netters and he came out of nowhere. He was sharp, quick and big."
The Sharks were also helped by a quick whistle on what appeared to be a Blackhawks goal during the second period. Viktor Stalberg thought he had a go-ahead goal, but the referee blew his whistle to stop play before the puck entered the net.
"The ref blew the whistle a little early. It's a shame, but that happens," Stalberg said. "We have 50 more games to have it even out. That's a game-changer right there. It's too bad. It's just the way things seem to be going for me right now."
Both teams entered having each scored 18 goals in their previous five games.
Niemi and Crawford were up to the task, and the teams combined for only six penalty minutes.
Clowe's goal gave the Sharks an early lead midway through the first period. He one-timed a pass from Jason Demers into the upper left corner. Clowe has points in six of seven games.
"Clowe did a lot of the grunt work," Sharks coach Todd McLellan said. "The good sign for us is we found our legs a little bit later in the game and found a way to win."
Hendry, who played for the first time in 14 games, took advantage by scoring his first goal off an assist from Jake Dowell. Hendry flared the puck, but it found a hole between Niemi's left skate and the post.
"It would have been a lot better with a victory, but of course you'll take a goal whenever you can get it," Hendry said. "It's been a while since I played, and I just wanted to get out there and create some speed and energy for the fourth line there."
Crawford stopped a point-blank shot from Patrick Marleau to keep the game tied midway through the third period.
- Chicago D Jassen Cullimore and C Dave Bolland returned after missing a practice.
- Vlasic has three assists in two games after going scoreless through the first 27 games of the season.
- Clowe was named the Sharks' player of the month for November.
- Blackhawks F John Scott assisted on Hendry's goal, his first point in 21 games.
- The Blackhawks had eight goals in their previous 24 power plays before getting shut out on two opportunities against the Sharks.