Nikita Kucherov scored an empty-net goal with 49.6 seconds left for the Lightning (41-26-5), who jumped over the Boston Bruins and pulled within two points of the Florida Panthers for the Atlantic Division lead.
Bishop has 17 shutouts in his NHL career, including one each with the St. Louis Blues and Ottawa Senators.
"The PK came up big tonight with some key blocks in opportune times," said Bishop, who has allowed two goals or less in eight of the past 11 games. "We talked about it on Friday and obviously we weren't happy with the way we played in Dallas (a 4-3 loss on Thursday).
"We came out tonight and played one of our best periods, if not the best period of the year in the first, and now it's about doing that for three periods. It's better to win 1-0 than to lose 4-3."