Bobby Wood also scored his second of the season for Salt Lake (3-0-1, 10 points), which assumed the top spot in the Western conference with the victory to build on last year's unexpected playoff run to the West final.
Zac MacMath made seven saves to preserve RSL's third consecutive win.
Walker Zimmerman scored his first goal of the season for Nashville (1-1-2, 4 points), which has lost two in a row and is midway through an eight-match road trip to begin the season before opening a new stadium.
The visitors are already halfway to last season's loss total, after they finished third in the Eastern Conference while tying an MLS record with 18 draws.
The 24-year-old Schmitt had never scored in MLS prior to his stoppage-time winner in last week's 3-2 win at New England.
In his 14th MLS appearance, his heroics arrived nine minutes after halftime.
Nashville cleared the danger from an initial Salt Lake corner kick. But on the second phase of play, Maikel Chang curled a cross from the right that bounded between multiple bodies on the way to the back post.
Schmitt met it by hammering a half-volley past goalkeeper Joe Willis from close range.
The visitors pressed for an equalizer, with MacMath intervening on several occasions, including a reflex save of Hany Mukhtar in the 56th minute and a sure-handed stop of Daniel Lovitz' flashing header 21 minutes later.
Wood gave Salt Lake the lead after only two minutes when he reached Justin Meram's corner kick at the near corner of the 6-yard box and powered a header beyond Willis.
Nashville went on the front foot and were rewarded with Zimmerman's leveler 23 minutes later from another dead-ball situation.
This time it was Zimmerman leaping higher than Wood to meet Mukhtar's free kick from the right and drive his own header past McMath.