Clyde meekly surrendered their ten match unbeaten run against a Peterhead side who have now replaced The Bully Wee in top place in the league table.
Clyde got off to the worst possible start, when Gilfillan placed the ball in the path of Rodgers to coolly slot the ball home under the body of Rajovic.
This stung the home side to life and The Bully Wee were quickly on level terms when Ferguson expertly converted a through ball past 'keeper Smith.
Any hopes the home support had of seeing their favourites gain control of the match disappeared when a Rodgers header looped over Rajovic into the net in the 13th minute. Indeed, the deficit could have got worse when a great strike from Rodgers struck the bar but the teams went in at the interval with the away side 2-1 up.
Clyde have shown great determination in recent weeks but The Bully Wee were unable to respond in similar fashion in this game.
Peterhead further stretched their lead in the 66th minute when Donaldson headed home an inswinging corner that the defence were unable to clear.
That goal proved to be decisive and the visitors were able to play out the remainder of the match in relative ease, with The Blue Toon jumping over Clyde to go top in League Two.
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HALF-TIME DRAW WINNING NUMBERS: 1st 2880 (cash prize), 2nd 2834 (£25 voucher), 3rd 3749 (signed ball)