Joyce was furious on Sunday when he was run out despite footage indicating fielder Mohammad Nabi had crossed the boundary rope when fielding the ball.
Two days later the 37-year-old batted for Ireland's entire innings, with Gary Wilson's 58 helping them post 265-5.
In reply, Afghanistan could only make 253-9 at a sweltering Stormont.
Joyce's 148-ball innings, which included three sixes and 19 fours, is the second highest in Ireland's one-day history behind Paul Stirling's 177 against Canada six years ago.
Sussex batsman Joyce also hit a century in Ireland's other victory in the five-match series.
After skipper William Porterfield and Sean Terry were dismissed cheaply to leave Ireland on 44-2, Joyce and Wilson put on 134 for the third wicket.
