Gary Hackett made one change to the starting line-up from last Saturday's draw with Trafford, fit-again Reece Hales returning in place of Josh Quaynor, who had to make do with a place on the bench.
Stourbridge made the best possible start to the game with Knight low angled drive from 30 yards finding its way past Jake Turner in the Gingerbreads' goal, and for much of the first half the Glassboys managed to keep the home side at arms' length.
However, Grantham began to exert pressure as the interval approached and were rewarded on 40 minutes. A cross from the right wing was spilled by Dean Coleman and although Liam Read couldn't manage to force his header over the line, Danny Meadows was on hand to turn in the loose ball.
There were early chances for both sides after the break. First Turner saved well from Kayelden Brown, and then Coleman redeemed his earlier slip with an equally good save from Meadows. Both Brown and Meadows will perhaps feel they should have done better.
And there was a late scare for the Glassboys on 87 minutes when Coleman once again had to be alert to tip Read's effort over the bar and ensure that the points were shared.
The result means that Stourbridge remain 11th in the Evo-Stik League Premier Division table, nine points adrift of the final play-off place.
Stourbridge: Coleman, Benbow (Morgan-Parker 73), Richards, Williams, Brown, Miles, Connolly, Broadhurst, Hales (Smikle 64), Canavan (Fitzpatrick 73), Knight.
Unused substitutes: Quaynor, Kenny.
Attendance: 208.