Goals either side of half-time from James Forrest and Beram Kayal helped Celtic FC get off the mark in UEFA Champions League Group H.
Forrest opened the scoring just before the break from the penalty spot and Kayal's deflected shot eight minutes after the restart means Neil Lennon's team move above AFC Ajax and into third place. Joy was tempered by substitute Nir Biton's straight red card and Lasse Schöne's 94th-minute reply, but the relief at full time was palpable.
Celtic had struggled to make early inroads, save for on 13 minutes when Teemu Pukki stole in front of Jöel Veltman, making his first UEFA Champions League start at centre-back, but the forward misdirected Mikael Lustig's cross.
Christian Poulsen is a more familiar name in the Ajax XI and he was orchestrating every move from the back. The Danish international almost broke the deadlock after 21 minutes. A free-kick from the visitors' left was touched on and Poulsen, arriving at the back post, saw his effort cannon back off the woodwork with Fraser Forster beaten.
Celtic upped their game and pushed for the opener. It came two minutes before half-time. The Ajax defence failed to clear their lines from a corner and as the ball broke to Anthony Stokes, the Irishman was brought down by Stefano Denswil for a penalty. After a delay Forrest displayed nerves of steel to power the ball high past Jasper Cillessen.
The Scottish champions continued on the front foot after the interval, with Forrest surging past Daley Blind before his cross was cleared to safety. Giorgios Samaras provided the same threat on the other side, so a second goal looked imminent. It arrived only after a scare at the other end when Forster darted off his line to smother an effort from Thulani Serero.
Almost immediately Samaras delivered a cross that was half-cleared, the ball breaking to Kayal whose shot was deflected past Cillessen by Denswil. With their last-16 hopes slipping away, it was the cue for Ajax to push on. Kolbeinn Sigthórrson fired wide on the turn from ten metres, Siem de Jong fizzed an attempt narrowly past the post and Serero was again denied.
Celtic's defence, superbly marshalled by Virgil van Dijk, held on until Biton saw red after a full-blooded challenge on Serero two minutes from time. Substitute Schöne halved the deficit with a fine swerving strike but it was too late to inspire a comeback. Ajax are now four points off second spot.