On an afternoon when the hosts were buoyed by the news of Milan Mandaric's takeover, goals from Beevers and Miller in the first-half set the Owls on the way into the 3rd Round.
McKay struck 11 minutes after the break before injury-time goals from Miller for Wednesday and Thornton for the Cobblers.
Northampton's cup adventures come to an end for the season and focus turns back to the relegation battle in League Two when Stockport come to Sixfields next weekend.