Annan equalised in the 47th minute against the run of play, when Harty found the top corner with a rasping drive from the right-hand side.
After 50 minutes, Montrose were reduced to 10 men when Alan Cambell saw red for handball and Harty stepped up to coolly slot home the resulting penalty.
Annan Athletic: Summersgill, Muirhead, Peter Watson, Neilson, Steven Sloan (Bell 61), Gilfillan, Jardine, Docherty, Cox, Harty, O'Connor (Felvus 69). Subs Not Used: Jamieson, Aitken, Steele.
Booked: Jardine.
Goals: Harty 47, 52 pen.
Montrose: Gonzalez, McNalley, Tweed (Nicol 61), Cambell, Pope, Hegarty (McCord 78), Crawford, Sinclair, Cameron, Tosh (Crighton 81), Boyle. Subs Not Used: Wood, Thompson.
Sent Off: Cambell (50).
Booked: McNalley.
Goals: Tosh 21.
Att: 473
Ref: Anthony Law
Source: BBC Sport
Source: BBC Sport