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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.
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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.
After Wilson's departure, Kevin O'Brien, making his 100th one-day appearance for Ireland, holed out to Najibullah Zadran for only one off Nabi's bowling.
Stirling quickly departed, but Stuart Poynter (12 no) stayed with Joyce to the finish as Ireland posted a total that was ultimately beyond the visitors.
Zadran top-scored for the tourists with 54, O'Brien gaining some solace for his failure with the bat by claiming three wickets.
Afghanistan were in trouble at 119-6 but rallied with a seventh-wicket partnership of 94, before losing their last three wickets in quick succession.
Ireland will be in action next in one-day games against Pakistan at Malahide on 18 and 20 August.
Ed Joyce responded to his controversial run-out on Sunday with an unbeaten 160 that helped Ireland earn a 2-2 one-day series draw against Afghanistan.