Steven Stamkos also scored for the Lightning (14-6-2), who are 8-2-1 at home.
Killorn scored the go-ahead goal with 1:53 remaining in the second period when he redirected a shot from defenseman Anton Stralman past Wild goalie Darcy Kuemper. The goal was Killorn's fourth in the past four games and sixth of the season.
"This felt good, especially after those last two games we didn't play the way we wanted to," Killorn said, referring to losses at the Toronto Maple Leafs (5-2 on Thursday) and the New York Islanders (5-2 on Tuesday).
"I think the outcome was great, but I think we stuck to the way we've been playing for most of the season. We were able to generate some opportunities by using our legs and skating hard to get into the right positions."
The Wild (11-8-0) took a 1-0 lead at 3:11 of the second period when Zach Parise scored his seventh goal of the season off a nice play by Thomas Vanek. Vanek took a pass from Parise in the slot and faked a shot to force Bishop to commit before passing back to Parise for the one-timer into an open net.
Stamkos tied the game at 13:42 of the second period with a power-play goal. He skated into the right circle and sent a wrist shot by Kuemper with Ryan Callahan providing a screen.
"We really did a good job to change the momentum in the second period and we realized what we're capable of when we utilize our speed and play down low," Stamkos said. "We were all over them, then they took a couple of penalties and we had the puck. I thought even in the third, outside of the last couple of minutes, we didn't [lift] our foot off the gas. It was a tight game and it is nice to get rewarded."
Bishop's biggest save came in the third period when he stopped Wild wing Nino Niederreiter on a shot in front of the net during a power play. Niederreiter took control of the puck when the Lightning failed to clear the zone and had a clear shot, but Bishop blocked it with his glove.
The Wild were 0-for-3 on the power play, and Parise said they could have done more with the opportunities.
"We aren't supporting each other very well," Parise said. "It's a lot of sitting around waiting for someone else to do something. We just stand around and look at each other … we don't retrieve pucks … it has kind of been a theme for us."
"The guys just got tough and decided not to let in a goal," Stralman said. "Guys like [Brian] Boyle and [Cedric] Paquette did what they had to do in that final minute. It was a crazy finish and [Bishop] was solid all game."
Kuemper finished with 26 saves for the Wild, who play at the Florida Panthers on Monday.
"I thought for the most part we played a pretty good game but the difference was a minus-1 on special teams," Wild coach Mike Yeo said. "We knew they we're going to be desperate, they played a good game. In the end you can't come in on a team like that, score one goal and expect to win."
Stralman had two assists for the Lightning, and Callahan had an assist, his eighth of the season.
"I thought we had lots of energy, I was very happy with our effort and the way we got to the puck," Lightning coach Jon Cooper said. "I thought it was an outstanding response, especially with the travel tribulations we had getting out of Toronto."