The Colombian winger grabbed the fourth and final game of the encounter after Kurt Zouma headed Stoke ahead seconds before the halftime whistle in the first half.
Maxim Choupo-Moting opened the scoring 27 minutes after a moment of quality allowed the striker to slip in and give the Potters the lead.
The hosts replied with a moment of quality of their own, when Davy Propper glided past the entire Stoke team to set up Pascal Gross for an easy goal.
Equally matched at the start
Both sides got off to a bright start in the opening five minutes, as Brighton and Stoke almost came close to nicking vital early goals.
Glenn Murray came inches away from poking the ball past Lee Grant after the striker found himself at the end of a Izquierdo cross, but the Seagulls forward missed the ball.
Moments later at the other end of the pitch, Choupo-Moting was denied by Lewis Dunk who managed to block the former Schalke striker’s strike from close range, and the resulting corner was eventually scrambled away by Matthew Ryan.
The Australian keeper was called into action six minutes later, when a great cross from Darren Fletcher found the head of Ryan Shawcross, whose header forced a fantastic save from Ryan as the Brighton shot-stopper tipped the ball over the bar.
Izquierdo was next to test his luck in finding the opening goal. He found himself through on goal after a smart pass from Propper released the attacker, but Izquierdo's curling effort in front of goal flew just wide of the far post.
A goal out of nothing
Despite encouraging signs, it was the visitors that drew first blood, as Choupo-Moting slotted the visitors ahead with a goal out of nothing.
Xherdan Shaqiri spotted the Cameroonian unmarked just outside of the box, and picked out his team-mate perfectly with a long ball. With an incredible first touch, Choupo-Moting was able to control the ball perfectly and finish past a surprised Ryan to give the Potters the lead.
Brighton should have been given the chance to level the game seven minutes before half-time, as Murray was clattered into by Shawcross inside the penalty area. But instead of awarding a penalty, referee Lee Mason pointed to the corner flag, causing uproar amongst the home fans.
A wild end to the first-half
Stoke’s lead wouldn’t last for long, though, as summer signing Gross levelled things up for the hosts two minutes before half-time.
The goal all came from Propper, who managed to take on the entire Potters midfield and defence. The Dutchman danced his way through the final third and a weak cross into the box found Gross. The German's strike flew through the legs of Grant, and put Brighton back on level terms.
However, the jubilation from the home fans would only last for a few seconds, as Zouma headed Stoke back into the lead from a corner deep into first-half stoppage time.
A messy corner in the dying seconds saw the ball fly towards an open Zouma and the on-loan Chelsea defender's simple finish from six-yards out put the Potters back into the lead.
Izquierdo levels it for Brighton
The Seagulls had been in the game from minute one of the match, and despite allowing Stoke to take the lead twice, Chris Hughton’s side remained dangerous and resilient to get goals throughout the evening, and that mentality was what got them their second equaliser of the evening.
Some poor defending from Zouma allowed Murray to lay the ball off to Izquierdo deep in the Stoke penalty area and he was allowed to tango his way though the mass of bodies in the area and slot the ball through the legs of Grant to make it 2-2.
With the game drawing to a close, neither side looked determined to find the fifth goal that would had won the game. Stoke resorted to keeping everyone behind the ball and breaking once possession was won, while Brighton were comfortable with keeping the ball in Stoke’s half.
Despite attacking changes, neither side could find a final goal as they were forced to settle for a point apiece.