Chasing 237 for victory, Ireland lost early wickets to be reeling at 29 for 3, but the pair showed all their experience in a stand which was the highest for Ireland in a home one-day international.
There was no repeat of the batting collapse which had handed Afghanistan the win on Tuesday, as Joyce, O'Brien and Paul Stirling all batted with great composure in a nerveless run chase.
After winning the toss and batting Mohammad Shahzad held together the Afghan innings again as the pugnacious opener showed his class with 10 fours in his 81.
Early wickets for Barry McCarthy, Kevin O'Brien and Andy McBrine meant that the visitors didn't get too far away before a 76-run stand between Shahzad and his skipper Stanikzai (33) gave their innings some impetus in the middle overs.
Paul Stirling bowling
Shahzad's effort was ended by Peter Chase however runs down the order from Mohammad Nabi (40) and Rashid Khan (24) dragged Afghanistan to 236 before the last wicket fell at the start of the 50th over.
O'Brien and McCarthy who shared eight wickets in Tuesday's defeat split six more here; the former with 3-28 and McCarthy 3-57; while Chase returned 2-68. McBrine (1-22) was also on the scoresheet while Tim Murtagh (1-31 from 10) was again impressive with the new ball.
Cut by Ed Joyce
Things looked ominous again for the home team after skipper William Porterfield (1) and Sean Terry (3) were both dismissed early by Hamid Hassan (2-21), and when Nabi dismissed Stuart Poynter, Ireland were in deep trouble.
Cometh the hour, cometh Joyce and O'Brien however and the pair batted together for 29 overs to restore order.
Their partnership was finally broken when Dawlat Zadran had O'Brien caught by namesake, Najibullah for 75 (10 fours) but Joyce went to and beyond his century as he and Paul Stirling did the rest. The Sussex batsman hit 8 fours and a six on his way to an unbeaten 105 with Stirling adding 39 not out (5 fours) at the other end.
It was Joyce's third ODI century - his 8th overall for Ireland - following hundreds against Pakistan in Dublin and Zimbabwe in Hobart.
Boundary for Kevin O'Brien
It was a morale-boosting win for John Bracewell's charges and it set up Sunday's penultimate game nicely insofar as the series itself is concerned.