It was Bishop's second shutout of the season for the Lightning (38-19-6), who are three points behind the Montreal Canadiens for first place in the Eastern Conference having played two more games.
Bishop continued his strong play from the Lightning's recent Western Conference road trip and has won his past four starts.
"I wasn't happy with my last couple of games at home, so it was nice to have this performance in front of the home fans," Bishop said. "I thought the team played well, we played a full 60 minutes with penalty kill, power play and 5-on-5, so it was good to see."
Chicago (37-21-5) lost for the first time in three games.
"It wasn't our best game, and in a game like this we have to keep it simple, and it just seemed like we were playing into their hands too much," Blackhawks defenseman Duncan Keith said. "They have a lot of speed and skill on all the lines. They can all skate and they can all make plays. We had to be a lot simpler tonight."
Brian Boyle scored his 13th goal of the season at 8:27 of the second period. He was camped in front of the net and put a behind-the-back pass from Jonathan Drouin past Blackhawks goalie Scott Darling.
"I was getting out to forecheck and I saw him coming up, so I put on the brakes and found myself open," Boyle said. "I had a good feeling he was going to get it out to me but I didn't think it would be as nice as it was. It was a heck of a play, a ridiculous play … pretty much anyone can put that in the net."
Stamkos made it 2-0 at 17:53 of the second period when he redirected a slap shot from the point by Jason Garrison.
"I thought we came out strong, I think we had a couple of penalties and that probably fired us up," Stamkos said. "It was an energetic crowd, they have a big following, and I think the goal quieted some of the fans wearing red. It was a good shot from Garrison."
Stamkos' second, his 34th of the season, came on a power play at 17:15 of the third period when he put a wrist shot over Darling's shoulder for the 4-0 lead.
Ryan Callahan scored a power-play goal 7:37 into the third period.
"It was good to see the power play working tonight, and we were doing more of what we've been practicing," Stamkos said. "Everyone is moving a lot more and trying to get in the right position to make things happen. It's something we always work on, but sometimes guys are standing in place during the game and you can't do that."
"Obviously their guy, Bishop, played well and he's a big goaltender that handles the puck well," Blackhawks wing Patrick Sharp said. "But we needed to help our guy out more and we could have done a better job of getting in front of him and getting better scoring chances. We didn't have enough jam around that net and it resulted in no goals scored."
The Lightning went 6-4-2 in February, all against Western Conference opponents.
"This month had been circled on the calendar," Lightning coach Jon Cooper said. "I know it wasn't divisional opponents, but it was eight road games, four at home, and I think at the time we played them, nine of them were in the playoffs. So that was a big game for us. We came out of it about .500 and I think it was a good measuring stick for us."