The hosts easily shaded the opening half to establish a two-goal cushion by the break, which should have been more.
Tom Brighton had a goal chalked off for an alleged foul against his marker Du Wei in what seemed a fair tussle for the ball, before Clyde had another effort disallowed for offside.
The incidents were soon forgotten after Eddie Malone and Stephen O'Donnell combined to set up the opener in the 32nd minute.
Malone's cross eluded Alex Williams but Craig Bryson was on hand to power a header past Artur Boruc.
O'Donnell then had a penalty saved by Boruc after Wei pulled down Brighton and oddly escaped any form of punishment from the referee.
O'Donnell took the resultant corner which led to Malone hammering home Clyde's second.
The Bully Wee maintained their aggressive approach after the restart and Brighton broke away to fire a shot inches over the bar.
Celtic tried to up the tempo in search of a breakthrough, but the home defence remained resolute and held out comfortably until the 82nd minute, when Peter Cherrie was finally beaten by Celtic substitute Maciej Zurawski.
The Bhoys never looked the part and Keane's hopes of becoming an instant hero ended in disappointment.
But for the Clyde fans who stayed after the game, all their players were heroes.