Defeat would have dragged the Bully Wee down towards the relegation zone at the foot of the cinch League 1 table.
But instead their 2-0 victory put daylight between Danny Lennon’s side and their rivals, opening up a five-point gap over second bottom Peterhead with East Fife a further two points back.
The Fifers were the better team for large parts of this match.
But their failure to find the net saw them let Clyde depart the kingdom with all three points thanks to a 2-0 win.
Clyde managed to stay in the game thanks to East Fife’s failure to kill them off and the one thing the Bully Wee always have is an attacking threat.
They have players who can hurt opponents in the final third and did just that at Bayview, although for once it wasn’t David Goodwillie who did the damage as Cunningham netted twice late in the game.
There had been a suggestion that should the Fifers go behind, and eventually lose, to Clyde then a poisonous atmosphere may develop inside the ground.
That never happened, an indication that the home support were generally satisfied with the effort on show.
Andrew Osei-Bonsu had a couple of sights at goal during a first half the home side dominated.
Kevin Smith was another who went close with a header which went just wide.
A header from Robert Jones which drifted inches over Jude Smith’s bar was the best Clyde could offer in the opening period.
But the visitors started the second half much brighter and Euan Deveney went close a couple of minutes after the restart.
East Fife managed to weather the early storm and went on to dominate again, but without asking too many questions of the Bully Wee backline
They were punished in the closing stages of the match.
On 73 minutes Goodwillie found Cunningham on the edge of the box and he sent a terrific drive beyond Smith.
Victory was sealed just four minutes later when Cunningham was in the right place at the right time and finished from close range.