Birmingham went into the tie after winning their four previous games this season, but really struggled to get a grip on the Saints.
Midfielder Lallana cracked home a deserved second goal just days after he grabbed the winner against Derby at Pride Park.
The skilful winger skipped past the static Liam Ridgewell in the Birmingham defence before smashing the ball past goalkeeper Colin Doyle and into the bottom left-hand corner.
The south coast club had taken the lead in the 17th minute after a wonderful flowing move.
Right-back Lloyd James crossed from the right to David McGoldrick who headed the ball back to Lee Holmes.
Midfielder Holmes controlled the ball on the edge of the area before hitting a low left-footed shot past Doyle and into the bottom corner.
Birmingham had their best chance of the half on the 30 minute mark which saw Garry O'Connor let fly with a 25-yard effort that fizzed just over the bar.
The goalscorers Holmes and Lallana linked up six minutes later and they should have given Southampton a 2-0 lead going into the break.
Holmes put a free-kick into the danger area and Lallana hit a right-footed shot that hit the crossbar.
The ball fell straight back to him but his first-time effort on the rebound hit the right-hand post and bounced clear for a free-kick.
Former Southampton striker Kevin Phillips came on at the break for the disappointing O'Connor but barley touched the ball in the second half and it was left for Lallana to finish off the game and give the Saints a well deserved 2-0 victory.