The 3-2 lead was short lived as Nashville tied it up at 12:31 on Trenin's tally. After exiting the puck out of their zone and counter attacking, Tanner Jeannot jetted up the ice and sent a centering feed into the low slot. Trenin tapped in the pass through Varlamov.
As both teams vied back-and-forth in the waning and fast-paced final minutes of the period, the Predators pulled out the shocking comeback win with 11.5 seconds on the clock.
Nashville circled the puck around the Islanders' zone and an attempted clearing attempt was stopped by Roman Josi. Josi sent a wrister into traffic and Tolvanen connected his stick with the shot to redirect it past Varlamov.
Nashville's prior goals were scored in the span of 1:24 in the first period, both ignited by forcing an offensive turnover from the Islanders and ushering a quick counterattack.
The Islanders had gone from holding a 1-0 lead to entering the first intermission with a 2-1 deficit to the Predators.
After chipping the puck out of their zone and pressuring the Islanders' defensemen, the Preds took advantage of a turnover by Luke Kunin. Kunin stripped Aho of the puck, cut to the slot and dropped the puck on the doorstep for Johansen to bury past Varlamov at 17:28.
The Predators capitalized on their second tally just 1:24 after Johansen's tying goal. Varlamov kicked out a rebound on Jeannot's long-range one timer, but a wide-open Sissons buried the puck on the back door at 18:52.
With the loss, the Islanders are still in search of their first win on home ice.
"We've had games in this building we could have won, and for whatever reason we haven't closed it out," Lee said. "There are a lot of individual games you look at and how close they were and we came out on the wrong side and it just happens to be that we strung them together in this building."