Dan Fitchett's strike was the difference as Salisbury saw off Grimsby in the Conference Premier.
The visitors edged the possession battle in the first half but failed to make the breakthrough.
That allowed the hosts to regroup at half-time, and they quickly took the lead in the second half when Fitchett rifled the ball in from three yards.
Andy Cook missed a glorious opportunity to equalise when he hit the crossbar from close range late on.
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Salisbury City manager Mikey Harris told BBC Wiltshire
"I'm really, really pleased with the lads. This group of players has got such a fantastic attitude.
"Dan (Fitchett) is on fire at the moment. I think that goal was coming to be honest; we had a good spell at the end of the first-half and we started the second-half really well.
"I'm disappointed we didn't go on and get a second. They way we defended as a team, everyone put their bodies on the line."
Grimsby Town manager Paul Hurst talking to BBC Radio Humberside's Matt Dean:
"Frustrated, I think the game was there for us today. I thought we didn't play quick enough and didn't realise that the game was there to be won. First-half it was a little bit pedestrian, we had enough of the game for sure but at the end we were pushing but the goal just after half-time makes it an uphill task for us.
"Judging it from a neutral turning up and saying who deserved to win, I don't think you'll find someone who said that we wouldn't be at least worthy of a point but my frustration is that I don't think that as a group we saw the opportunity in front of us.
"I think from our point of view it was like when we were on the ball it was almost like a touch-touch stand and watch where we are going to play it and then play it. I think when you're confident and on form and you're flying then you step onto things and you know exactly where that next pass is we're just too slow in our play. "
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