Riley Sheahan, Drew Miller, Pavel Datsyuk and Danny DeKeyser scored for the Red Wings. They can close out the Eastern Conference matchup by winning Game 6 at home Monday night.
The shutout was the second of the series for the young Mrazek, who had no previous NHL playoff experience before being named Detroit's starter over veteran Jimmy Howard. The 23-year-old goalie blanked the Lightning 3-0 in Game 3 at home and also had the only shutout against the league's highest-scoring team during the regular season.
It was a frustrating evening for Tampa Bay, which rallied to win Game 4 on the road, evening the series after fizzling in Game 3 and being outplayed for 54 minutes before being rescued by Tyler Johnson on Thursday night.
Sheahan and Datsyuk scored on the power play. Miller's first goal of the series made it 2-0 through the second period, and DeKeyser added an empty-net goal with 1:38 remaining.