It was Vejmelka’s ninth NHL shutout.
Anders Lee scored in his Utah debut, Michael Carcone had a goal and an assist, and Clayton Keller had two assists for the Mammoth, who have won all three home openers in franchise history.
Arvid Soderblom made 26 saves for the Blackhawks (0-2-0), who have lost the first two games of their season-opening three-game road trip, including 5-2 at the Vegas Golden Knights on Tuesday.
Guenther gave Utah a 1-0 lead on the power play at 16:41 of the first period. He took a pass from Logan Cooley and snapped a shot from the top of the right face-off circle.
Carcone scored from low in the left circle 40 seconds later to push it to 2-0 at 17:21, converting a pass from Kevin Stenlund.
Nick Schmaltz then made it 3-0 at 9:47 of the second period when he put a rebound over the pad of Soderblom from the right side.
Lee extended the margin to 4-0 at 13:06, scoring with a tip in the slot.
The forward signed a three-year, $16.2 million contract ($5.4 million average annual value) with the Mammoth on July 1 after playing all 14 his previous NHL seasons with the New York Islanders.
Guenther scored his second power-play goal of the game at 15:28, redirecting a pass from Clayton Keller to make it 5-0.
Daniil But made it a 6-0 final at 12:50 of the third period by deflecting a Carcone shot.
