Danny North's injury-time equaliser denied 10-man Shrewsbury a victory.
Defender Colin Murdock was sent off for a professional foul on 56 minutes after bringing North down.
But Grimsby's Peter Till had to clear Kelvin Langmead's header off the line and keeper Phil Barnes needed to pull off a fine save to thwart Marc Pugh.
Guy Madjo scored after Barnes fumbled Dave Hibbert's shot, before North diverted Danny Boshell's shot past Shrews keeper Glynn Garner to equalise.
Grimsby: Barnes, Hird (Till 46), Atkinson, Fenton, Newey, Hegarty, Bolland (Boshell 26), Hunt, Clarke (Taylor 66), Jones, North.
Subs Not Used: Montgomery, Bennett.
Goals: North 90.
Shrewsbury: Garner, Herd, Murdock, Langmead, Tierney, Humphrey (Kempson 58), Hall, McIntyre, Davies, Madjo (Darren Moss 90), Pugh (Hibbert 71).
Subs Not Used: Esson, Hunt.
Sent Off: Murdock (56).
Goals: Madjo 75.
Ref: David Foster (Tyne & Wear).