Parker also had a career-high 18 assists in the win, which put San Antonio up 2-0 as the series moves to Memphis Saturday.
The Spurs scored only nine points in the fourth quarter and watched a 13-point lead evaporate, but Duncan scored six points in overtime while the Grizzlies went 0-for-4 from 3-point range in the extra time.
Conley's jumper with 18.2 seconds left in regulation tied the game 85-85 and sent the game into overtime.
Beautician charged with giving client fatal silicone butt injection
LGBT community has 'bullied the American people': Bachmann