The Amsterdam club dealt a potentially fatal blow in the Eredivisie race as it narrowly defeated Ronald Koeman's side.
The 176th edition of the Klassieker saw Frank de Boer's side pick up three points against Feyenoord to move eight points clear of second-placed Twente.
Graziano Pelle, who was allowed to play after having a one-match ban for his outburst at Twente last week suspended for 12 months, put the hosts ahead on the half-hour mark with his 19th league goal of the season.
However, the sides went in level at the break, as Kolbeinn Sigthorsson equalized on the stroke of halftime. Ajax completed its comeback courtesy of Joel Veltman, whose 72nd minute goal ensured the team extended its unbeaten league run to 14 matches.
The Amsterdam club's hopes of retaining the title were further boosted as Twente was held to a 1-1 draw at Utrecht. Quincy Promes had put the visitors ahead in the 18th minute at the Stadion Galgenwaard, but Tommy Oar equalized almost immediately after halftime.
That result means Twente and third-placed Vitesse, which beat Roda JC on Saturday, are now both eight points adrift of Ajax with eight matches remaining.
RKC Waalwijk, meanwhile, remain embroiled in relegation trouble after falling to a 4-0 defeat to AZ at the AFAS Stadion.
Jeffrey Gouweleeuw and Nick Viergever had put the hosts into a two-goal lead by halftime, and that advantage was further stretched by Steven Berghuis' double.
Elsewhere, Elvis Manu's 77th minute penalty rescued a 1-1 draw for Cambuur at Groningen.