Saints manager Mauriccio Pellegrino made just one change from the side that beat Watford in the FA Cup on Saturday, with James Ward-Prowse replacing Sofiane Boufal.
Brighton meanwhile made a raft of changes from the weekend, with only Dale Stephens keeping his starting place from Saturday's late cup win at Middlesbrough.
It was Brighton who immediately took the initiative, Izquierdo blazing over inside the area after just 30 seconds following some slack Saints defending.
The visitors would indeed go on to take an early lead, Glenn Murray converting a 14th minute penalty for his seventh league goal of the season after Wesley Hoedt brought down Solly March inside the area.
That goal seemed to spark a response from Southampton, and James Ward-Prowse's fizzing cross into the Brighton area after 21 minutes perhaps deserved to end in something more than a corner that came to nothing.
Suddenly it was Southampton enjoying much of the possession and territory, but failing to make anything of note, Ryan Bertrand's effort from the left hand corner of the penalty which landed on the roof of the net after a promising run from the England international, before some quick thinking from Brighton keeper Matt Ryan bailed out Shane Duffy after the Irishman failed to control a pass.
The hosts were then almost gifted the flukiest of levellers, as Ryan hit his clearance against an onrushing Hojbjerg, with Brighton fans breathing a sigh of relief as the deflection cannoned off the crossbar.
Bertrand then went close from the edge of the area again with just minutes to go from half time, having received the ball following a training ground-esque move from a Ward-Prowse corner.
Southampton's struggles in the final third would prompt Pellegrino into a double change at half time, with Sofiane Boufal and new signing Guido Carillo replacing Dusan Tadic and Oriol Romeu.
Jack Stephens then went close to repeating his goalscoring feats of the weekend for Southampton, heading wide a Ward-Prowse cross from a dangerous position.
10 minutes later, Stephens would indeed repeat those goalscoring feats to get Southampton back on level terms, scrambling home a Ward-Prowse free kick from close range after Brighton's flimsy looking two-man wall deflected the ball into Stephen's path to give the home side a vital equaliser.
The hosts continued to put the pressure on in search of a lead, and Matt Ryan had to get his whole body behind Hojbjerg's low and powerful drive from 35 yards five minutes after the equaliser.
Though both sides continued to push for a winner, the two were forced to settle for a point apiece, leaving both firmly involved in the bottom half fight to avoid relegation.