But the majority in the Amex Stadium were convinced the home side should have been awarded a 39th-minute penalty when referee Lee Mason ignored claims Ryan Shawcross had brought Glenn Murray down inside the area.
Maxim Choupo-Moting gave the visitors the lead with a low finish past Mat Ryan but Brighton, who have not beaten Stoke since 2001, equalised after 43 minutes when Pascal Gross swept through the legs of goalkeeper Lee Grant, deputising for the injured Jack Butland.
A lofted ball from Dale Stephens fell to Murray who smartly passed to Izquierdo, his initial shot rebounded back to him and at the second time of asking curled the ball into the net for a deserved leveller.
The visitors took the lead in the 27th minute through Cameroonian global Eric Choupo-Moting who capitalised on poor defending to put Stoke ahead after he was set up by Xherdan Shaqiri.
Five minutes after the restart, Ramadan created a great chance, however, his effort was saved by Ryan.
Albion's celebrations were swiftly snuffed out, however, as poor defending allowed Kurt Zouma to head home and restore Stoke's lead in first-half stoppage-time.
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Stoke piled the pressure on towards the end and Allen had a fine opportunity present itself to him seven minutes from time, but his fierce volley was inadvertently blocked by Peter Crouch in what proved to be their final chance.
Chris Hughton is still without the injured Steve Sidwell ahead of Brighton's first competitive meeting with Stoke since 2011, when Stoke won 3-0 in the fifth round of the FA Cup.
Nevertheless, just before the interval Brighton hauled themselves level courtesy of a third goal of the season for Gross.
- Xherdan Shaqiri has been involved in more Premier League goals in 11 games this season (2 goals, 5 assists) than he was in 21 appearances in the competition last season (4 goals, 2 assists).
- Fletcher was also playing in his 103rd consecutive match in the competition - the outright 5th longest such run for an outfield player.