Albion twice fought back after falling behind, first when Pascal Gross cancelled out Eric Maxim Choupo-Moting’s opening goal, and then when Izquierdo struck after Kurt Zouma had restored Stoke’s lead.
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.
The stalemate meant both side’s consolidated recent progress.
And for Stoke manager Mark Hughes, it also meant his side avoided equalling the club’s worst Premier League start after 12 games.
Defeat would have turned the focus on Hughes’s position once again and the manager needs no reminding of the fact that four of the five clubs below Stoke before last night’s match have already made changes in the dug-out
A positive run of results meant Hughton and his players headed into the international break on a high and that confidence was reflected in a starting line-up that was unchanged for a fourth successive game.
Stoke had also shown signs of improvement before the break, recovering twice to claim a point against Leicester after securing a first away win of the season at Watford.
Mark Hughes would have liked to have followed Hughton’s lead in naming an unchanged team but Jack Butland’s finger injury sustained during an England training session meant Lee Grant deputised for the keeper.
Both sides had an early chance to consolidate their recent form with Stoke in particular quickly proving a threat by forcing two early corners that unsettled the home side.
A long-range shot from Brighton midfielder Dale Stephens flew narrowly wide but it soon became clear the home side’s threat would come from the flanks and in particular from Jose Izquierdo down the left.
The Colombian repeatedly found space behind wing-back Mame Diouf but lacked the composure to produce the final ball that would have allowed Brighton to take an early lead.
And when he cut inside after being set free by Davey Propper in the 18th minute, he placed his shot wide of the far post with Pascal Gross and Anthony Knockaert better positioned on the edge of the box.
Propper then headed straight at Grant from Knockaert’s free-kick before Brighton’s promising start was brought to an abrupt halt in the 28th minute when Choupo-Moting put Stoke ahead.
There was little sign of danger when Darren Fletcher squared the ball to Shaqiri on the halfway line, but the Swiss’s pass floated over the top of the Brighton backline was brought down superbly by Choupo-Moting who found space between the centre-backs before producing an assured finish.
It was the kind of goal that would have infuriated Hughton and the Brighton manager had further cause for disappointment when referee Lee Mason waved away a strong appeal for a penalty when Glenn Murray went down under a challenge by Ryan Shawcross.
The manager’s mood was lifted two minutes before the break when Albion levelled.
A strong run by Propper took the Dutchman through the Stoke midfield and out to the right hand flank where he pulled a low ball back towards Gross who swept the ball home first time from 12 yards.
A loss of concentration in first half added time, however, ensured Stoke restored their lead before the interval after a Fletcher corner again caused problems with the ball bouncing towards Zouma who headed home from close range.
Hughton will have made his feelings known in the dressing room at half time but the message didn’t initially appear to get through with Ramadan Sobhi missing a good chance to extend Stoke’s lead in the 49th minute.
But Brighton ramped up the p-ressure and levelled when Zouma played Murray onside at a free-kick, allowing the striker to tee up Izquierdo who scored at the second attempt.
