Argyle goalkeeper Jake Cole also saved a spot-kick for the Pilgrims.
Argyle took the lead in the fourth minute after Dale defender Ryan Edwards conceded a penalty by handling Scott Griffiths' low driven cross.
Edwards' team-mates were adamant he had slipped on to the ball but their protests were dismissed by referee Gary Sutton and Madjo converted the spot-kick.
Three minutes later, the Pilgrims went further ahead with Andres Gurrieri scoring for the second successive home game. The little Argentinean rose higher than his taller markers to powerfully head Paris Cowan-Hall's cross past Dale keeper Josh Lillis.
Rochdale wasted an opportunity to reduce the deficit 10 minutes after the break when Bobby Grant's weak penalty, after Jason Kennedy had been fouled by Max Blanchard, was well saved by Jake Cole.
They were given a lifeline in the 76th minute when Dele Adebola headed home Andrew Tutte's free-kick, but Madjo's second penalty of the game, after Ryan Edwards had fouled Joe Lennox, made the three points safe.
