The defending champions started the day seven points adrift of Philip Cocu's side but goals from Mike van der Hoorn and Richairo Zivkovic means they go into the mid-season break just four behind.
Ajax started slowly at the Stadio Woudestein and needed Japser Cillessen to keep them in the game with two saves from Ninos Gouriye.
Frank de Boer's substitutions breathed new life into the visitors, though, and two of those introduced struck to secure the win.
Just 60 seconds after coming on, Van der Hoorn broke the deadlock 83 minutes in before fellow sub Zivkovic doubled the advantage in the final minute with his first goal for the club.
Colin Kazim-Richards struck the decisive goal in their 1-0 win after 32 minutes - the Turkish striker's seventh goal of the campaign and fourth in as many league matches.
Vitesse recorded their first win since mid-October with a comprehensive display against Heracles as three first-half goals secured a 3-0 victory at the GelreDome.
Bertrand Traore's brace took his tally to five in his last three matches, while Zakaria Labyad also got himself on the scoresheet.
Youness Mokhtar opened the scoring for Alfred Schreuder's side after 12 minutes, but, with nine minutes to play, they found themselves 2-1 behind and down to 10 men after Renato Tapia's dismissal.
