Frolik connected on a wrist shot in the second period and then tipped in the decisive goal with 5:02 left in the contest.
Rookie Jacob Trouba tied the game 4-4 earlier in the third period with his first NHL goal.
Mark Scheivele and Bryan Little also scored for the Jets. Ondrej Pavelec stopped 34 of 38 shots in the game. He allowed four goals on 24 shots in the first two periods but shut the Oilers out in the third period.
Devan Dubnyk made 23 saves for Edmonton and allowed all five scores. Jesse Joensuu scored a power-play goal at 7:53 of the second period to give the Oilers a 4-2 lead but that was the last time the home team crossed the crease.