At Blundell Park, Danny Wilson's side needed just a point to go above Queens Park Rangers and into the automatic promotion places but a tenth victory on the trot - coupled with a Plymouth defeat - would send them top.
The Robins got off to a great start as Scottish striker Lee Miller put the visitors in front 10 minutes in, but their early lead was soon pegged back, as the managerless Mariners earned a penalty mid-way through the half.
Iain Anderson would equalise from the spot on 31 minutes, as both sides went into the break at 1-1.
The second half saw the West Country club push for a winner and not for the first time this season, Bristol City made a late breakthrough to snatch victory.
Aaron Brown struck with two minutes remaining to secure The Robins all three points and take the Ashton Gate side a point above Plymouth at the top of the table, while Grimsby remain only four points above the drop zone.
The Pilgrims came off the summit following an unforgettable 3-0 defeat to Tranmere Rovers at Prenton Park.
Brian Little's side picked up from their FA Cup success against Swansea City on Saturday to record a huge win against Paul Sturrock's side.
Frenchman Eugene Dadi put Rovers in front on 19 minutes before Cup hero Iain Hume doubled the Merseyside club's lead four minutes later.
Dadi then made it 3-0 seven minutes after the break to seal a win that takes Tranmere into mid-table and seven points adrift of the play-off places while Plymouth drop to second in the table.
Click below for match stats:
Division Two
Grimsby Town 1-2 Bristol City
Tranmere Rovers 3-0 Plymouth Argyle
Click here for an updated Division Two table.
