But Martin Foyle's men were level within six minutes when David McGurk struck with a close-range shot.
Brodie secured the win from the spot after being brought down by Greg Young.
The Minstermen could have taken the lead straight after the break but referee Andy Madley waved away Brodie's protests after he was brought down in the area.
City's top scorer, who has netted 20 times in the Blue Square Premier this season, also had a header cleared off the line before then having a goal ruled out for offside.
Ingham, Purkiss, McGurk, Graham, Meredith, Harsley, Clarke (Lawless 66), Barrett, Pitt (Carruthers 82), Gash (Rankine 66), Brodie. Subs Not Used: Parslow, Smith.
Goals: McGurk 69, Brodie 90 pen.
Altrincham: Coburn, Williams, Smith, Young, Densmore, Danylyk, Doran (McAliskey 77), Lawton, Brown, Little (Denham 60), Senior (Carden 77). Subs Not Used: Saunders, Welch.
Booked: Young, Brown.
Goals: Denham 63.
Ref: Andy Madley (West Yorkshire).