The game at the Amsterdam ArenA looked set to be another frustrating chapter in a disappointing season for Frank de Boer's team.
But Anwar El Ghazi headed an 82nd-minute winner to move his team 11 points behind runaway leaders PSV Eindhoven.
Utrecht were Sunday's big winners with a thumping 6-2 triumph over AZ.
The UEFA Europa League hopefuls were blown away during the opening stages as Willem Janssen and Mark Diemers netted before a Sebastien Haller penalty made it 3-0 to Utrecht in the 17th minute.
Haller was on target from the spot once more after Aron Johannsson reduced the deficit and a Kristoffer Peterson own goal in the 83rd minute made it 5-1.
Utrecht's Gevero Markiet was the next man to put through his own net, but the hosts had the final word as Edouard Duplan struck a minute from time.
Feyenoord moved up to third place at AZ’s expense thanks to a 3-0 victory over NAC Breda.
Fred Rutten's team took a 10th-minute lead through Lex Immers, whose goal was the first to be confirmed by the HawkEye goalline technology system in the Eredivisie.
Mitchell Te Vrede hit a second-half brace for the hosts to seal second-bottom NAC's fate.
Elsewhere, Albert Rusnak and Tiaronn Chery scored to give Groningen a 2-0 win over basement boys Dordrecht.
