Smith gave Vegas the lead at 16:22 of the third period when he swept the loose rebound of Mitch Marner's shot past Dallas goalie Casey DeSmith's right pad.
Brayden McNabb and Ivan Barbashev each scored, and Adin Hill made 13 saves for Vegas (32-25-14), which is 3-6-0 in its past nine games.
The regulation win moved Vegas into second place in the Pacific Division, one point ahead of the Edmonton Oilers.
Wyatt Johnston and Justin Hryckowian each scored, and Casey DeSmith made 30 saves for Dallas (43-16-11), which has two regulation losses in its past 19 games (15-2-2).
Dallas remains in second place in the Central Division, five points behind the Colorado Avalanche.
McNabb gave Vegas a 1-0 lead at 4:01 of the first period on a snap shot from the bottom of the left face-off circle after skating through three Dallas defensive sticks.
Johnston tied it 1-1 at 10:55 with a power-play goal. Johnston finished off a tic-tac-toe passing play with Matt Duchene and Miro Heiskanen. Heiskanen's pass from above the right circle found Duchene behind the goal line, who set Johnston up for the snap shot from the slot.
It was Johnston's League-leading 23rd power-play goal of the season and surpassed Dino Ciccarelli (22) for the Dallas/Minnesota North Stars franchise record for most power-play goals in a season.
Hryckowian gave Dallas a 2-1 lead at 16:48 when he chipped in the rebound of Colin Blackwell's shot from the high slot, putting a wrist shot around the right pad of Hill.
Barbashev tied it 2-2 at 9:10 of the second period when Brett Howden's cross-crease pass found him at the right post for the sharp angle, top shelf snap shot that beat DeSmith.
