Gary McSheffrey half-volleyed City into the lead after just five minutes, an early opener which was missed by around 200 or more protesting Sky Blues fans who had gathered outside.
It was a peaceful demonstration aimed at under-fire owners SISU, calling on fans to show their support in favour of a change of ownership at the cash-strapped club between 2.45 and 3.15, with around 30 fans boycotting the third-round tie entirely by remaining outside.
Yet those present inside, an attendance of 9,000 which included 1,700 in the away end, were present to see 17-year-old midfielder James Ward-Prowse level shortly after the hour mark for a youthful Saints side.
And, just as a replay was rightfully looking on the cards, defender Aaron Martin headed home an 82nd-minute winner to book Southampton's place in Sunday's fourth round draw.
It was, however, a much closer affair than a glance at the npower Championship table would have suggested as top edged past bottom.
Coventry boss Andy Thorn made four changes to his XI, most notably top scorer Lukas Jutkiewicz - heavily linked with a January switch to hometown club Southampton - missing out due to a back injury.
Saints, minus suspended 17-goal striker Rickie Lambert, brought in five new faces, youngsters Ward-Prowse and Ryan Doble among those coming in.
But it was incoming goalkeeper Bartosz Bialkowski who proved his worth after just four minutes as he denied City striker Roy O'Donovan when clean through.
Yet the Sky Blues - donning a 1987-inspired replica kit to mark the 25th anniversary of their famous Wembley triumph over Tottenham - were not to be denied for much longer.
Cyrus Christie sent in a cross from the right and, with Saints appealing for a foul, Gael Bigirimana's header set up McSheffrey and he half-volleyed home from 12 yards.
Coventry remained in control as the majority of protesters outside started to filter into the stands, just in time to see Richard Wood head over from McSheffrey's corner.
Morgan Schneiderlin fired narrowly wide in the 35th minute as Southampton offered a rare threat in the final third, while Coventry's Gary Deegan was denied by Bialkowski towards the end of an ordinary first half.
City keeper Chris Dunn was called upon to make his first real save within 60 seconds of a frantic start to the second half as he denied Ward-Prowse.
But the lively youngster made no mistake from close range in the 64th minute as he converted a cross from former Coventry full-back Danny Fox.
Dan Harding volleyed an effort inches wide moments later before Carl Baker drilled just over at the other end as both sides went in search of a winner.
And it went Southampton's way eight minutes from time as Martin met Fox's outswinging corner and his header squirmed over the line despite the best efforts of Dunn.