The tie allowed the Sabres to remain unbeaten on a four-game road trip.
Miller, a 22-year-old rookie, made 22 saves Tuesday in his first shutout at Minnesota. He was perfect over the first two periods against the Sharks, who exploded in the third and challenged relentlessly in overtime.
Miller preserved the tie in regulation and faced five shots in the extra period. He stopped a slapper by defenseman Dan McGillis with just over two minutes remaining, and turned away Cheechoo twice in the final 90 seconds.
Buffalo moved to 2
Nabokov stopped 23 shots and also produced impressive saves in the extra session. He made diving stops on Miroslav Satan and Alexei Zhitnik in the final two minutes, and caught a break when another shot by Satan hit the post.