With the game out of hand, manager Craig Counsell turned to Tellez to finish off the victory, which clinched a postseason trip for the fifth time in six years.
"Cy Young candidate, ya know," Tellez said after throwing a scoreless ninth inning in which he allowed one hit and one walk and struck out Jesus Sanchez, who swung and missed on a 63 mph fastball.
Tellez said his appearance on the mound came after a quick conversation with Counsell, who asked in the seventh inning if the 6-foot-4, 270-pound slugger can throw strikes.
"I said yes. Absolutely," Tellez recounted.
Despite having to borrow left-hander Wade Miley's glove, Tellez said he didn't have any nerves and drew inspiration from a Hall of Fame pitcher.
"Sit on the corners, watch [Greg] Maddux work," Tellez said he told catcher Victor Caratini.
"They're already tweeting Cy Young candidate," Tellez jokingly told a teammate.
The win went to 2021 Cy Young Award winner Corbin Burnes, who threw five scoreless innings and was backed by a 12-run second inning that put things out of reach early.
"Twelve runs -- I didn't know that was possible," said Burnes, who had not won since July 20. "Obviously, it makes the next innings go a little easier."
Milwaukee sent 15 batters to the plate in the second against relievers Steven Okert (3-2) and Bryan Hoeing during the second-largest inning in team history. The Brewers scored 13 runs in the fifth to beat the California Angels 20-7 on July 8, 1990.
Two-run homers by Josh Donaldson and Christian Yelich started and capped the scoring. Mark Canha also hit a two-run double, Carlos Santana and Blake Perkins added RBI doubles, and William Contreras, Sal Frelick and Brice Turang had run-scoring singles. In his second at-bat of the inning, Donaldson had another RBI with a groundout.
The Brewers have won four straight and cut their magic number to clinch the National League Central to one.
Information from The Associated Press was used in this report.