Falkirk 1 Celtic 0
A Steve Thomson strike early in the first half was enough to give the Bairns their first win in eight games.
The home side should have taken the lead after only two minutes when a neat one-two between Carl Finnigan and Russell Latapy saw the former through on goal but his shot went just wide of the mark.
Celtic immediately raced to the other end and some neat play on the edge of the box by Shunsuke Nakamura ended with the Japanese star firing in a snap-shot that was superbly saved by Kasper Schmeichel.
In the fifth minute Celtic were awarded a penalty when Craig Beattie was fouled by Dean Holden as he was about to pull the trigger. However, Schmeichel again pulled off an excellent save to deny Beattie from the spot.
Celtic again went close to taking the lead on 14 minutes when Paul Hartley's cross from the left was missed by everyone and rebounded back off the post and into the arms of Schmeichel.
Despite the visitors' pressure it was Falkirk who took the lead two minutes later when Finnigan burst down the right and sent a pinpoint cross for Thomson to head powerfully past Artur Boruc.
Celtic looked to get back on level terms but excellent defending by Holden and Darren Barr denied Beattie and Kenny Miller on two separate occasions.
An incident just before half-time saw both sides reduced to 10 men when Finnigan and Stephen McManus clashed on the edge of the Celtic box and both were given their marching orders.
Celtic should have had another penalty early in the second half when Nakamura was tripped by Patrick Cregg inside the box but referee John Underhill waved play on.
The visitors continued to bombard the Falkirk goal in a desperate bid for the equaliser with Nakamura and Beattie both going close.
Bhoys boss Gordon Strachan then introduced his three substitutes in a last-gasp bid to salvage something from the game but it was to no avail as the Bairns held out for a famous win.