David Unsworth's men made hard work of beating National League North outfit Chester over the two ties.
After Saturday's 1-1 draw at Boundary Park, over 500 fans travelled to the replay at the Deva Stadium three days later and endured an even more tense affair.
It started well for Latics, as it has done so many times this season, with Ben Tollitt scoring his fifth goal of the season after 10 minutes to take the lead.
Willoughby’s reply on the hour for the home side took the game to extra time.
Chester led for the first time in the match after 99 minutes through Kevin Roberts and looked to be heading to victory, before Mike Fondop’s late equaliser two minutes from time took the game to penalties.
Tollit, Dan Gardner, David Okagbue all scored before Fondop’s effort was saved.
But with Chester having missed two earlier efforts, it was left to Chris Porter, who was returning to the side after injury and came on as substitute in extra time, to score the fifth penalty and seal Latics' progress.
Latics will now travel to the Racecourse Ground on the weekend of November 5 to play Wrexham for the second time this season.
Having lost 2-1 in the league earlier this season, they will be hoping to avenge the result by winning a place in the FA Cup second round.
Latics host Yeovil Town on Saturday in a return to National League action.
