Howden won it after stealing the puck in the right circle and scoring on a wrist shot following Reilly Smith’s high-sticking penalty at 3:42.
Howden’s goal came after Pavel Dorofeyev completed the hat trick for Vegas at 19:07 of the third period to tie it 4-4 when he found a loose puck in front of the net with Carter Hart pulled for the extra attacker.
Shea Theodore had a goal and an assist, and Jack Eichel had two assists for the Golden Knights, who are the No. 1 seed from the Pacific Division. Hart made 34 saves.
Dylan Guenther, Lawson Crouse and Michael Carcone scored for the Mammoth, who are the first wild card in the West. Clayton Keller had two assists, and Karel Vejmelka made 31 saves.
Vegas leads the best-of-7 series 3-2. Game 6 will be at Delta Center in Salt Lake City on Friday (10 p.m. ET; Utah16, SCRIPPS, ESPN, TVAS2, SN360, SN).
John Marino gave Utah a 1-0 lead at 17:11 of the first period. He recovered Keller’s shot off the end boards and scored off Hart’s right pad.
Dorofeyev’s power-play goal tied it 1-1 at 19:19 with a wrist shot that went bar down.
Crouse put the Mammoth back ahead 2-1 at 10:40 of the second period on a wrist shot from the high slot off a feed from Keller.
Dorofeyev’s second goal of the game tied it 2-2 at 15:37. Theodore dropped the puck from below the goal line to Dorofeyev, who roofed a wrist shot.
Theodore gave Vegas a 3-2 lead at 17:17 on a wrist shot from the high slot.
Guenther tied it 3-3 at 5:54 of the third period. Defenseman MacKenzie Weegar flipped the puck into the neutral zone to Kailer Yamamoto, who found Guenther with a cross-ice pass on the rush.
Carcone put Utah ahead 4-3 at 12:42 with a one-timer on a 2-on-1 rush.
