Oldfield latched onto a Jamie Lyon chip kick before running 40 metres untouched as the Sea Eagles rallied from 13 points down to emerge victorious 19-13.
Oldfield's try came 60 seconds after Manly halfback Daly Cherry-Evans had levelled the scores with an equally unlikely left-footed field goal from the right-footed kicker.
A field goal to halfback Wade Graham right on halftime looked like being the difference as the Sharks battled hard in a physical contest in front of 15,133 people.
Cronulla skipped out to a 13-0 lead thanks to tries to winger Matthew Wright and hooker Stuart Flanagan and looked to be heading for a comfortable victory before the visitors started to mount a comeback in the 61st minute when Kieran Foran pounced on an Oldfield kick.
Oldfield himself had scooped up a scrappy grubber from Glenn Stewart as the Sea Eagles edged their way back into the game.
Six minutes later, on the back of four straight penalties, Manly crossed again - this time through burly prop George Rose who crashed over from five metres out, cutting the lead to just one.
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