Cup winners in 2013, the year they were relegated from the top flight, Wigan led 2-0 at halftime.
Northern Ireland striker Will Grigg put them ahead in only the fourth minute and just before the half-hour mark a free kick by former Manchester United midfielder Nick Powell was deflected in by Bournemouth's American Emerson Hyndman.
The home side, who have only just moved out of the Premier League relegation places, had risked making eight changes.
They made two more with substitutions for the second half and got a goal back through Frenchman Lys Mousset.
Ryan Fraser's free kick then came back off a post, but defender Steve Cook earned a replay in the 92nd minute.
(Reporting by Steve Tongue; Editing by Christian Radnedge)
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