"He's been chasing up a little bit the last couple of days," said Stange, who got the save after earning the win in the series' first two games.
The Bees mobbed each other on the field before putting on goggles for the postgame party in their plastic-covered clubhouse, where they sprayed champagne and beer on each other.
"It means a lot. It's a big accomplishment," Stange said. "It's been a good series. It was fun and a good group of guys."
Buckner, who earned the win, allowed two runs on five hits to outduel 51s starter Aaron Harang, who allowed three runs on six hits in six innings.
Tommy Field hit a towering tiebreaking homer off Harang in the fifth to give Salt Lake a 3-2 lead and it didn't trail again.
The Bees added an insurance run in the seventh, when Luis Rodriguez drilled an RBI double to make it 4-2. Luke Carlin scored on the play after singling and taking second on a sacrifice bunt. Field, who drew a walk, was thrown out trying to score.
The 51s scored a run in the eighth to make it 4-3 as Ruben Tejada and Mike Baxter belted consecutive doubles off Dustin Richardson. Baxter took third on a groundout, but Jeremy Berg got Jamie Hoffmann to ground out to second with the infield in and then struck out Rylan Sandoval looking to end the threat.
Salt Lake had the highest ERA in the PCL in the regular season, but its pitching especially the bullpen has come up big in the playoffs.
"Regardless of our team ERA, over the year a lot of guys got better," a soaked Bees manager Keith Johnson said. "Our bullpen's been the strength of our team all year. Once again, they were able to close thing thing out for us tonight."
Salt Lake scored twice in the fourth to take a 2-1 lead. Matt Long and Rodriguez singled to open the inning and Efren Navarro followed with a tying sacrifice fly. Roberto Lopez singled and Scott Cousins drove in a run on a force out.
The Bees will face the Omaha Storm Chasers for the PCL championship in a best-of-five series that starts Tuesday in Nebraska. Omaha, which went 70-74 in the regular season, swept the league-leading Oklahoma City RedHawks, who went 82-62.
Salt Lake will host Game 3 on Friday at Spring Mobile Ballpark.
"It's going to be a good series," Johnson said. "Their ballclub does a lot of things similar to what we do. They have real good pitching, and we're going to have to find a way to grind out some runs and pitch and play defense behind them.
"All year with this group, every single guy that's come in has bought in to what we were doing. We've got a ragtag bunch of guys out there and they all play for each other."
Storylines Bees 4, 51s 3
R Billy Buckner allows two runs on five hits to earn the win.
• Salt Lake will face Omaha in the PCL championship series.