Gopperth's strike saw Newcastle battle back from 19-12 down to beat Sale 22-19 and cut the gap at the bottom of the Aviva Premiership between themselves and Wasps to just four points.
With Dean Richards, who takes over from Gary Gold as Falcons director of rugby next season, and Newcastle United manager Alan Pardew in the stands, the Falcons stretched their unbeaten home run to five games with a huge second-half performance.
Sale scored three terrific first-half tries, but led only 19-12 at half-time after giving away and hatful of penalties which led to a warning from referee David Rose.
Gopperth gave Newcastle the lead in the opening minute with a penalty but Sale then scored twice in the space of eight minutes, both tries sparked by searing breaks from scrum-half Dwayne Peel.
The first ended with a beautifully-worked score in the corner from Johnny Leota after Sam Tuitupou's wide run and perfectly-delivered pass, and the second try came after Peel stepped outside and then in to have Newcastle on the back foot and Nick Macleod's clever crossfield kick opened the Falcons defence for James Gaskell to score in the other corner. Macleod converted for a 12-3 lead.
But Sale then conceded four penalties in six minutes and Gopperth kicked two, missed one and hit the post with the other for 12-9, before the Falcons fly-half missed Tuitupou who linked with Tom Brady for Rob Miller to run in Sale's third and Macleod again converted.
Newcastle thought they had scored with a big drive over the Sale line but it was ruled out by the fourth official, but Gopperth kicked his fourth penalty when Sale were penalised at the scrum.
Two minutes into the second half Macleod missed a penalty after failing with one just before the break, and it looked like proving costly, with Tim Swinson being driven over for Newcastle's first try in the 53rd minute and Gopperth levelling the scores at 19-19 with the conversion.
Newcastle battered away and Gopperth missed a 68th-minute penalty and a had a drop goal attempt charged down before stepping up with four minutes left on the clock to strike his fifth penalty and clinch victory.
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