United should have been awarded a penalty after 15 minutes when Owen was pulled back as he skipped past a defender in the 18-yard area but the referee ruled otherwise.
The ball was immediately punted down the other end where Lewis was adjudged to have handled outside his area - again another contentious call.
The wall did its job and Matt Endersby's shot from the loose ball flashed wide.
Rovers forced a couple of corners and belied their lowly position with some threatening attacking play.
Evesham too were looking good going forward and Fitter, operating in a central role, fired wide after good work from Owen and Dean Wellington after 23 minutes.
Owen was again involved five minutes later when he set up Steve Lutz whose angled shot was narrowly off target.
It was Owen again who tormented the visiting rearguard and this time the hosts got their reward when Steve Duncan rose highest to head in the striker's 31st minute overhead kick.
Liam Givans had a great chance to make it 2-0 two minutes later but shot over after Lutz had helped on Fitter's dead-ball strike.
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