Southampton had twice taken the lead in the first half at Kenilworth Road through Matt Oakley and Kenwyne Jones only for the Hatters to level through Kevin Nicholls and Ahmet Brkovic.
And lively Luton saw their positive second-half display rewarded when new free signing from Reading, Morgan, curled home a beautiful 25-yard strike in injury time.
Boosted by their win at Crystal Palace on Saturday, the Hatters started brightly and Warren Feeney tested Antti Niemi after just four minutes when he latched on to Kevin Foley's long ball and fired at the Saints goalkeeper from eight yards.
Steve Robinson then fired in a 30-yard effort that Niemi comfortably held before Southampton's first effort saw Rory Delap's volley tipped aside after a deep left-wing cross from Danny Higginbotham.
Higginbotham was involved again as the visitors took the lead in the 18th minute when the full-back raced to the byline to pull back for Oakley to fire home from just inside the penalty area.
Luton regrouped and only two breathtaking saves from Niemi, firstly from Warren Feeney's 35th minute header and then from Robinson's 39th minute effort, kept the Town out.
The Hatters equalised when the hardworking Feeney laid off for Nicholls to drill home from 10 yards in the 41st minute.
But that good work was undone when rookie home goalkeeper Dean Brill mis-judged a Dennis Wise cross in added time and Jones nodded home.
Luton went back on level terms seven minutes after the break when Brkovic met Nicholls' in-swinging free-kick at the far post for his second of the season.
And Town continued to pepper the Southampton goal with Feeney, Howard and Morgan all going close.
Brkovic almost netted again when he got on the end of another dangerous Nicholls free-kick but this time his header hit a defender and drifted just wide.
The Hatters were not to be denied though and Morgan collected a ball from substitute Enoch Showunmi, turned inside Wise and found the top corner in style.