McKenna made 28 saves for his first NHL shutout, and Roberts scored in the third period in the Lightning's 1-0 victory over the New York Islanders on Saturday night.
McKenna was making his second career NHL start and third appearance overall.
"I have experienced that at other levels, but never in the NHL," McKenna said. "It's hard even to describe. It's quite a feeling."
Roberts, playing in his second game after missing 28 games with a left elbow injury, redirected Steve Eminger's shot with 6:26 left.
"My game's always been trying to get to the net and get some ugly goals," said Roberts, who scored his first goal since Nov. 10 and the 437th of his NHL career. "I was fortunate tonight."
The Lightning stopped a four-game losing streak.
Yann Danis stopped 27 shots for the Islanders, who have lost two in a row following a four-game winning streak. Danis won his previous four starts.
"It's never fun to lose like that in the third," Danis said. "We played a good game. We battled hard. There's definitely some positives out of it."
Tampa Bay starting goalie Mike Smith missed his third straight game because of an undisclosed upper-body injury. Lightning general manager Brian Lawton said Smith is expected to practice by Monday and could play soon after.
"He's progressing nicely," Lawton said.
McKenna stopped a right-circle shot by Trent Hunter and then used his stick to keep the loose puck from going into the net in the second. He also stopped a left-circle shot in the final minute by Kyle Okposo, who got the scoring chance right after serving a hooking penalty.
"How can you not root for a kid like that?" Tampa Bay interim coach Rick Tocchet said. "All of a sudden, now he's our starting goalie. Pretty unflappable kid. He's done a good job."
Danis made several strong saves, including an in-close chance by Martin St. Louis, when Tampa Bay kept the puck in the Islanders' zone for the entire 2 minutes of a first-period power play.
"He played great," Islanders coach Scott Gordon said. "In the first period he made some great saves. If we don't get that performance in the first period, the second and third probably don't even matter."
Tampa Bay defenseman Matt Smaby and Islanders enforcer Tim Jackman fought 4 seconds into the game. Jackman and Lightning star Vincent Lecavalier had a fight during New York's 3-1 win over the Lightning on Tuesday night.
Tampa Bay rookie C Steven Stamkos had an assist on his 19th birthday. ... The Lightning traded LW Jussi Jokinen to Carolina for LW Wade Brookbank, D Josef Melichar and a fourth-round draft pick. Lawton said Melichar will join Norfolk of the AHL, while it hasn't been decided where Brookbank will play. ... Islanders D Mark Streit and C Nate Thompson sat out with shoulder injuries. ... Tampa Bay D Andrej Meszaros (left arm) had his stretch of playing in 298 consecutive games end. ... New York LW Sean Bergenheim returned after missing the previous eight games with a strained side.