Melton just about deserved victory for a first half display in which they dominated the scrum and moved the ball well through the backs and forwards.
Wonderful line breaks by Martorano, Evans, Spence and Williams put Melton on the front foot, while the scrum drove Oakham back, allowing Wade to take several balls against the head.
Skipper Greaves bounced several would-be tacklers out of his way, while back row partners Peters and Prior added the more delicate touches. The front row of Kerr, Wade and Spence belied their combined age of 150-plus years with great performances.
Young half-backs Haywood and Grindey probed with useful breaks, and several times Grindey turned the Oakham team with good rolling kicks.
Clemmons drew his centre partner Freeston on to some lovely lines of running, and allowed wings Clarke and Forfar chances to run at Oakham, while full-back Williams ran the ball back strongly.
The forwards nearly got a pushover try, but moved too quickly to control the ball. But from the next scrum Wade took one against the head and the pack drove Oakham over the line.
Melton went further ahead when good handling from forwards and backs allowed Prior to score.
Just before half-time Oakham replied with a breakaway try to turn round at 17-7.
Both teams made several changes with Blagburn, Underwood and Farrish coming on in the backs and O’Reilly and Broughton came on in the forwards.
Melton struggled to get their game back together in a much tighter second half, and an Oakham try with 10 minutes left set up a grandstand finale.
But Melton held out to shade a keenly-fought and enjoyable match.