Sordell slid home a 64th-minute penalty and wrapped up victory nine minutes later as Dougie Freedman's men made sure of victory 10 days after blowing a two-goal lead in their Reebok Stadium clash.
Martin O'Neill had made his intentions clear by naming a strong side for the replay in contrast to Freedman, whose own slender play-off aspirations prompted him to make six changes from the weekend draw with Millwall.
MK Dons reached the fourth round for the first time in their short history with a 2-0 replay victory over Sheffield Wednesday.
Shaun Williams' first-half penalty and a fortuitous second goal from a Dean Bowditch free-kick saw the npower League One team overcome their Championship opponents at stadium:mk.
In a game of few chances, the hosts created the better opportunities as a much-changed Wednesday side struggled for cohesion.