St Johnstone had the better of the cagey opening exchanges with Jason Scotland's strength posing the home defence problems.
After 18 minutes, Stephen O'Donnell tested Kevin Cuthbert in the St Johnstone goal with a rasping effort from 25 yards. Two minutes later it was Saints' turn to threaten, but Scotland should have done better after a floated pass from Kevin James put him through on the goalkeeper.
A crude challenge on Chris Higgins saw the first yellow card of the match go to Scott Paterson after 27 minutes.
Steven Milne put the Perth side ahead on 32 minutes after a well-worked move. Clyde fans were calling for a foul after a strong but fair Scott Paterson challenge, but Scotland acted quickly, feeding the ball through to Ryan McCann whose ball from the right across goal left Milne with an easy tap-in.
Saints were looking lively and Darren Sheridan came close with a 20-yard drive two minutes after the restart.
Clyde needed a goal but the Saints became more dominant, and Simon Mensing was unlucky to see his header saved after a mesmerising interchange between Paul Sheerin and Sheridan 10 minutes into the second half.
Clyde were given hope 14 minutes from time when Paterson received a second yellow card for a foul on O'Donnell, but the home side could make nothing of the resulting free-kick.
Nine minutes from time, St Johnstone lost all discipline when Mensing was sent off for striking Alex Williams off the ball while referee Alan Freeland was preparing to book Milne for a reckless challenge on Eddie Malone.
Predictably, Clyde had the momentum and Craig Bryson took advantage of the space afforded to him to make a great run before seeing his shot rebound off the bar.
But Clyde's attacks, even with a two-man advantage were weak and infrequent, and Saints held out for three points.