Mellor dominated the match at Millgate Lane but were limited to a lone Tom Bright strike. Even then the ball was cleared from within the goal but had crossed the line.
The importance of the match seemed to affect Mellor, who never reached their full potential, despite exerting enormous pressure on the Bedians' defence.
Bedians started the stronger and Billy Riley had to be alert to block an early chance for the home side on four minutes.
Six minutes later Tom Bright volleyed a good chance three feet too high after a Sam Parker flick.
Mellor frustratingly then wasted two corners, dropping them behind the goal from the flag kick.
Tom Bright works a shooting chance
Mellor had far more possession but Bedians were dangerous on the break and on 17 minutes ex Mellor player Stuart Wright got beyond the defence and was upended by Steve Baguley for a penalty, duly converted.
Four minutes later Parker fed Bright whose shot was again too high.
Bedians' goal was under siege and on 28 minutes Andy Kuehl fired in from long range but the Bedians' keeper took it comfortably.
Kuehl's long range strike
On 30 minutes Parker wriggled free on the right but his shot hit the side netting.
Mellor's under worked keeper Immy Roberts then came out to clear a long ball but it fell to a Bedians player whose 40 yard shot towards the empty goal hit the crossbar.
Sam Healey then headed over from a Parker corner.
Parker on the attack
Mellor began the second half with increased urgency. They had two shots blocked on 50 minutes and a minuter later Parker was denied by a fine save.
On 62 minutes Bright made the breakthrough, forcing the ball home after a Rick Axford corner.
The build up to Mellor's goal
It should have been the platform for a winning finale and Marcus McNulty almost provided a second after a stunning run down the middle past three defenders.
But on 66 minutes a weak clearance saw Bedians score again from 22 yards.
Matt McNulty replaced brother Marcus on 68 minutes and three minutes later a Tom Bright header from an Axford corner was headed off the line.
Bedians' goal under siege
It was all hands to the pump now for Bedians as Matt McNulty headed yet another corner against the angle of post and bar.
On 80 minutes Ian Arnfield replaced Bright but despite several more frantic scrambles in the home side's six yard box Mellor could not find an equaliser.
Steve Whelan was Mellor's star man.
Mellor Firsts drew 4-4 at home to South Manchester after leading 4-1 with just 20 minutes left. The visitors played the entire match with 10 men after arriving short.
Mellor's goals came from a Matt Jamieson penalty, Carl Brindley and Jonny Cooke (2).
The Firsts play Cheadle Hulme Villa away on Wednesday and they are also Mellor's opponents in the Rhodes Cup Final if Mellor can eliminated Old Trafford in the semi. Villa beat Rochdalians 4-1 in their semi.
The Seconds beat Whitworth Park 2-0 in a friendly. Joe Maloney and James Robinshaw scored.
The Fourths lost 0-1 to Strets in their final league game of the season, finishing eighth in Division D.