Grimsby drew at Kidderminster to extend their unbeaten run to seven games, while Harriers are rooted to the foot of the Blue Square Bet Premier.
Danny Pilkington and Keith Briggs went close with headers for the hosts, while Town had chances at the other end.
Grimsby should have taken the lead when Andy Cook fired wide from close range after Joe Colbeck struck the crossbar.
Colbeck hit the bar again late on but Harriers held on to secure only their fourth point of the season.
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Grimsby Town joint boss Rob Scott told BBC Radio Humberside:
"I'm a bit disappointed to come away with (just) a point, but it's another game without defeat and another clean sheet, we just lacked that cutting edge today.
"We certainly miss someone that's going to stick it in the back of the net - Cook is low on confidence you can see that, but he's working hard.
"It just didn't fall nicely for us, and I think if we'd have scored, we'd have gone on to see the game out."