For the Bully Wee a victory would cut the Fifers five points adrift of them and allow some breathing space.
East Fife went into the game chasing a three points which would lift them off the foot of League One and, in doing so, send Clyde below them.
Ultimately it was the hosts who got it their way, coming back from going behind to hit three goals in the closing stages of the game.
Clyde started well and with just a couple of minutes gone Jude Smith did well to beat away David Goodwillie’s acrobatic effort.
However East Fife enjoyed the bulk of possession during the early stages but too often wasted the final ball.
With so much at stake for both sides, the cagey start to the game was understandable.
Apart from the early chance for Goodwillie, neither keeper was seriously troubled for the next 20 minutes.
East Fife’s best chance of the opening 45 minutes came ten minutes before the break when Scott Mercer broke into the Clyde box and picked out Kyle Connell but, before he could get his shot away, the Clyde defence were back to clear.
The Fifers ended the first half strongly, but it was the Bully Wee who created the first opening of the half. Goodwillie’s good work inside the box allowed him to pick out Ross Cunningham who had time and space but fired high over.
East Fife were worthy of their lead when it arrived on 57 minutes though. Neil Parry did well to get down and block Aaron Dunsmore’s shot but first to react was Connell who had a simple tap in.
Clyde reacted well and were level on 67 minutes as Goodwillie broke clear in behind the Fife defence and sent a terrific chip over Smith.
It got even better for the home side within two minutes when Cunningham put them ahead from a couple of yards out.
East Fife were all of a sudden chasing the game and Connell went close.
But by committing so many men up front they left gaps at the back and were exposed when Cunningham raced clear to make it 3-1.