The 11-times winners played a weakened side and looked in trouble after Richard Chaplow blasted home an unstoppable shot in the last minute of the first half, but United finished strongly to advance to Sunday's fifth-round draw.
Holders Chelsea needed a late equaliser by Salomon Kalou to snatch a 1-1 draw at Everton, while at the other end of the football spectrum Crawley became the first non-league team since 1994 to reach the last 16 when they beat League Two Torquay 1-0 away despite having two penalties saved.
Matthew Tubbs got the only goal late in the first half for Crawley, who had knocked out league clubs Swindon Town and Derby County in the previous two rounds.
Tubbs was one of the Crawley players to have a penalty saved by Scott Bevan in a match in which both sides had a man sent off.
In two more of the weekend's five all-Premier League ties, Aston Villa beat Blackburn Rovers 3-1 and Bolton Wanderers drew 0-0 at home with Wigan Athletic.
United manager Sir Alex Ferguson gave Danish keeper Anders Lindegaard his debut, opted for a reserve back four, and left Wayne Rooney, Dimitar Berbatov, Nani and Ryan Giggs on the bench.
It played into Southampton's hands, and after Chaplow unleashed a screaming shot into the top corner, the home fans were dreaming of an upset to match their 1976 Cup final victory over the same opponents.
Yet United, with Giggs and Nani introduced for the last half-hour, improved and levelled after 65 minutes from an Owen header.
Ten minutes later Giggs slid a pass perfectly into the path of Mexican striker Hernandez, who kept his cool as he stumbled to the ground to roll the ball under Southampton keeper Bartosz Bialkowski and inside the post.
"They played well, they're flying high in their division," Owen told ITV. "It's always tough in the cups in the first hour but they have to run more to keep up with us and it's often the way that the better teams come good in the last half-hour."
ANCELOTTI REACTION
Chelsea, bidding to be the first team to win the FA Cup in three successive seasons since Blackburn Rovers in 1884-86, played a full-strength team but looked flat all day and only good goalkeeping by Petr Cech kept them in the game.
Everton, unbeaten against them in five league games, took control after 62 minutes when Louis Saha powerfully headed in a corner.
Chelsea boss Carlo Ancelotti reacted by sending on Kalou in the 70th minute, and five minutes later the Ivorian finished off a swift counter-attack for the equaliser.
"The result was good, we were 1-0 down and it wasn't easy to come back into the game," Ancelotti told the club's website.
"Everton put strong pressure all the time on the pitch, used a lot of long balls, they were very dangerous on set-pieces and scored on one. It was a difficult game but we showed good spirit."
