Stanislav Varga then headed against the bar for Celtic before David Healy's long-range shot tested Artur Boruc in the Bhoys goal.
Celtic boss Gordon Strachan opted to rest many of his senior players, with Chris Sutton, Neil Lennon, John Hartson and Stilian Petrov all missing.
But the home fans got their first glimpse of new signing Paul Telfer, and on-loan Polish keeper Boruc also impressed.
Kevin Blackwell used his entire squad of 19 players during the game, with only Shaun Derry completing the full 90 minutes.
Celtic: Boruc, Telfer, McManus, Balde (Thompson h/t), Varga, McGeady (McParland 72), Gardyne, Lawson, Wallace, Beattie (Zurawski 63), Maloney.
Subs not used: Marshall, Aliadiare, McGlinchey, O'Dea.
Leeds: Bennett, Kelly (Richardson 68), Butler (Carlisle 84), Gregan (Kigallon 68), Harding (Crainey 78), Wright (Walton 86), Derry, Bakke (Spring 78), Lewis (Pugh 84), Blake (Ricketts 72), Healy (Einarsson 78).