 Hardie was on target for St Johnstone |
A second half goal from Martin Hardie kept St Johnstone's hopes of promotion to the Premier League alive. Saints looked jaded and the home side twice hit the woodwork through Steven Masterton and Andy Ferguson.
St Johnstone keeper Kevin Cuthbert was kept busy, while Clyde's David Hutton made impressive saves to deny Peter MacDonald and Jason Scotland.
Hardie smashed in a close range shot on 74 minutes to move the Saints three points behind league leaders Gretna.
Both sides have two matches remaining but Gretna also enjoy a far superior goal difference.
"I think we probably just shaded it," Saints manager Owen Coyle told BBC Sport.
"Clyde are a young team, full of energy and it was always going to be a difficult game for us.
"We've played an awful lot of games and the character and desire shown by my players after Saturday's Scottish Cup semi-final speaks volumes for them."
St Johnstone entertain Queen of the South, while Gretna are at home to Clyde on Saturday.
Clyde: Hutton, Harris, McCann (Arbuckle 67), MacLennan, McKeown, Masterton, Bryson, Gilmour, Williams (Ferguson 67), Imrie, Michael McGowan. Subs Not Used: David McGowan, McKenna, Cherrie.
Booked: Harris.
St Johnstone: Cuthbert, Anderson, Stanic, McInnes, Lawrie, James, Sheerin, Hardie, MacDonald (Lilley 70), Scotland (Jackson 85), McLaren. Subs Not Used: Milne, Monaghan, Halliwell.
Booked: Anderson, MacDonald.
Goal: Hardie 74.
Att: 1,352
Ref: Scott McDonald