They came from 2-1 behind to beat Exeter City 3-2 at home.
They will face the winners of Aldershot and Kingstonian in the next round.
Scott Chester put the MIghty Stags ahead early on but his effort was cancelled out by Morana and Grimes added another for Exeter.
In the second half however, Ollie Pascoe and Jack Odam grabbed the goals that saw AFC Totton reach the second round.
Elsewhere, Bermuda Under 17 international Jonte Smith hit a hat-trick for Crawley Town as they eased past Wycombe Wanderers.
Louis John grabbed the other goal for Crawley as they won 4-1 to progress to the next round.
Darlington were the biggest winners of the night though as they thrashed Sheffield 7-1.
There was also wins for Thurrock, Macclesfield Town, Oxford United and AFC Wimbledon last night.
Full FA Youth Cup First Round Results 02/11/11
Darlington 7 – 1 Sheffield
Kidderminster Harriers 4 – 2 Brighouse Town
Cheltenham Town 1 – 3 Oxford United