The Australia goalkeeper made a stunning 88th-minute penalty save from Charlie Adam at the bet365 Stadium, after Dale Stephens had pushed Jese Rodriguez, before Dunk denied the midfielder a tap in from the rebound with an excellent challenge.
This was surely a game Stoke should be winning if they are to navigate a route to safety, especially with matches coming up against Manchester City, Arsenal, Spurs.
Stoke remained in the relegation zone, while Brighton is three points better off.
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But Stoke could do little about the tricky winger's brilliant opener as Izquierdo played one-twos with Solly March and Stephens, before coolly slotting past Butland into the bottom-right corner.
Adam moved forward in slow motion and somehow contrived to see his shot blocked by Lewis Dunk in one of the most remarkable moments of the season so far.
Agonisingly for Stoke, Diouf's powerful header was goalbound but Knockaert did just enough to head off the line and preserve a point for the Seagulls.
- Jose Izquierdo has been directly involved in four of Brighton's last seven Premier League goals (2 goals, 2 assists).