Salford had finished three places and three points above the home side in the table.
However, the Mariners ended the season in great form and took the lead with their first foray forward when a cross from the right was headed clear as far as full-back Staunton, who sent a superb cushioned volley into the top corner from 25 yards out.
Karl Robinson’s men, who would have gone up automatically had they won at struggling Crawley on the final day, quickly recovered their composure and were level when the home side made a mess of dealing with a throw-in and Cesay, in for a first start since 31 January, kept his cool to slot in.
Neither side could force the goalkeepers into meaningful work for the rest of the half until Oluwo’s header from Luke Garbutt’s corner beat Smith.
Grimsby boss Dave Artell led the complaints about the goal being allowed to stand but referee Matthew Corlett was unmoved.
That seemed to take a lot of the energy out of the home side and they barely threatened in the second half, with midfielder Kieran Green’s tame free-kick straight at Matt Young in the Salford goal being their best effort.
The Mariners won both league games between these two sides in the regular season and will still believe they can turn the deficit around on Friday.