The Bees rallied from an early 3-0 deficit to stun Las Vegas, which had won 21 of its final 31 games during the regular season.
Meanwhile, Salt Lake entered its first postseason series since 2008 after losing 12 of its final 16 games.
Long's 325-foot homer dropped just over the right field fence just inside the foul pole and gave the Bees a 1-0 lead in the best-of-five series.
"I've faced Carson a lot and those guys throw a lot of breaking balls, especially to lefties," said Long. "So I was going up there looking for one up and got it.
"I didn't really get it all. I just hit it to the right part of the yard in the corner, down the line where it gets short. It was good placement, if anything."
Las Vegas manager Wally Backman just shook his head.
"You've got to tip your hat to Long," he said. "It was a slider that was up. ... You don't want to get beat on the pull side late in the game, but he wrapped it around that foul pole."
The Bees trailed all the way, until Scott Cousins' two-out single off Carson in the bottom of the eighth made it 3-3, setting the stage for Long.
"It's fitting," said Salt Lake manager Keith Johnson. "That's the way we played all year. We just grind it out."
According to Backman, another bad pitch against Cousins hurt Las Vegas.
"We had the right match-ups the match-ups we wanted," he said. "... With Cousins coming to bat, I wasn't too concerned. We know what kind of hitter he is and he looked bad on breaking balls. But then we throw him a fastball.
Johnson praised the effort of Salt Lake's pitchers, including starter Matt Shoemaker, who gave up four hits and walked three batters in the first three innings but kept the Bees in the game.
Salt Lake relievers Dustin Richardson, Jeremy Berg and Daniel Stange allowed only one hit over the final three innings.
Shoemaker "... found a way to get through six innings us us," Johnson said. "He didn't necessarily have his best stuff but he made pitches when he had to. And our bullpen did a great job just went after guys and got the outs we needed."
Backman used five pitchers in the final three innings behind starter Matt Fox, but the 51s' bullpen could not hold the lead.
O Salt Lake takes a 1-0 lead in its PCL playoff series against Las Vegas with a 4-3 win.
• Matt Long's two-out homer run in the bottom of the ninth gives the Bees the victory.
Wednesday • Salt Lake 4, Las Vegas 3
Thursday • Las Vegas at Salt Lake, 6:35 p.m.
Friday • Salt Lake at Las Vegas, 8:05 p.m.
Saturday • Salt Lake at Las Vegas, 1:05 p.m. (if necessary)
Sunday • Salt Lake at Las Vegas, 1:05 p.m. (if necessary)