Protas cut it to 4-1 at 10:36 when he muscled past Axel Sandin-Pellikka on the rush and beat Gibson with a far-side shot from the bottom of the left circle.
Fehervary made it 4-2 at 8:30 of the third period, scoring on a wrist shot from the right circle.
Jakob Chychrun appeared to pull Washington within 4-3 at 9:41, but the goal was waved off due to goaltender interference by Protas. The Capitals challenged, but the call was upheld after a video review.
Dylan Larkin scored into an empty net at 17:10 for the 5-2 final.
The teams will play the second of back-to-back games in Detroit on Sunday (1 p.m. ET; FDSNDET, MNMT, NHLN, TVAS).
“It was a good team win,” Leonard said. “Obviously it was good to get that lead early and tack on a couple more. You knew that they were going to have that push and they did, but for the most part I thought we did a good job weathering it and were able to cap it off.”
NOTES: Detroit outshot Washington 17-6 in the first. … Gibson improved to 7-0-0 in his past seven appearances, tying his career high for longest winning streak, set from Oct. 31-Nov. 16, 2021. He became the first Red Wings goalie with a streak that long since Joey MacDonald (7-0-0 from Feb. 8-28, 2012). … Detroit forward Alex DeBrincat had eight shots on goal and was plus-2. … Chychrun had eight shots on goal but was minus-3 in 21:31. Capitals center Dylan Strome was also minus-3, along with forward Alex Ovechkin, who was limited to two shots on goal.