Thompson made a big stop on Calle Jarnkrok and on the next Golden Knights rush, Eichel finished off a quick passing play with a one-timer from the left faceoff dot.
Blake Coleman was called for a hook on Nicolas Roy and then after a chat, the officials also sent Keegan Kolesar off for a five-minute major hit-to-the-head on Chris Tanev along the end boards.
However, after reviewing, they downgraded the penalty on Kolesar to a two-minute minor.
Tanev left the game but later returned.
With 34 seconds to go in the offsetting penalties, Rasmus Andersson was sent off for holding the stick giving the visitors 1:26 of PP time but the Flames killed it off.
Lucic had words with Kolesar early in the second period and was called for a hold on him and just as the penalty expired, Evgenii Dadonov put a rebound in from beside the net at 4:46.
Then Vegas got two quick ones off rushes, first Markstrom stopped William Karlsson but Michael Amadio swept home the rebound at 8:24, then Jonathan Marchessault tipped one in 40 seconds after.
Vladar came in for Markstrom after the fourth tally.
The Golden Knights struck on the powerplay with 2:24 to go in the middle stanza, Roy tipping it home.
Karlsson scored late in the third to finish things out.