They remain second-bottom, but the result moved them up to within eight points of Scunthorpe, who are currently just outside the drop zone.
Kiwi Rikki Bovey took five wickets as Grimsby were all out for 140, a total Alford reached for the loss of seven wickets.
Alford Ladies were beaten by 10 wickets at Market Rasen on Tuesday evening.
Caroline Smith top scored with 16 and Teresa Tate added an unbeaten 12 before the away side ended their 20 overs on 48-5. Table-topping Rasen reached a matchwinning total of 51 without losing a wicket.
Alford are in sixth spot.