The former Stockport and Motherwell manager was appointed on Monday night to replace Mark Cooper, to become Peterborough's third manager of the season, and will have been impressed with the battling qualities on display at London Road.
The visitors' slide down the table looks set to continue, however, after a lifeless performance which saw Posh goalkeeper Joe Lewis untested throughout the 90 minutes and captain Mikele Leigertwood and defender Peter Ramage dismissed.
However, despite picking up their first win since the start of December, Peterborough remain nine points adrift of safety at the foot of the table.
QPR boss Mick Harford handed debuts to new strikers Marcus Bent and Tamas Priskin after the duo signed on loan on deadline day but Rangers still lacked a cutting edge.
Bent was starting for his 13th league club but the journeyman has not scored since last Valentine's Day and showed no signs of ending hi drought at London Road.
The hosts settled first in a high-tempo start but it was Bent who had the first shot in anger, scuffing an effort horribly wide from 25 yards.
Gannon's side were looking bright and went ahead with a well-crafted goal in the ninth minute.
Craig Mackail-Smith chased a ball into the channel and did well to clip the ball back into the area and find Boyd.
The Posh captain had his back to goal but managed to lose his defender with a fine turn and coolly picked out Mclean in the six-yard box for a simple finish.
Boyd then played Mackail-Smith in with another clever pass but QPR goalkeeper Carl Ikeme was quick to come off his line and clear before another Boyd ball was fired over by Chris Whelpdale.
Rangers were struggling to contain Boyd in his role behind the front two but could have drawn level before the break when Matt Connolly was afforded the space for a free header from a corner but put his effort high over the crossbar.
Harford's side controlled the opening 15 minutes of the second half until Leigertwood was sent off on the hour mark.
Alejandro Faurlin overhit a pass in midfield and as Leigertwood stretched to regain possession he caught Posh winger Tommy Rowe with a high and late challenge.
Referee Danny McDermid instantly produced the red card and the hosts took the initiative, with Boyd and Mackail-Smith both going close with good efforts.
Ramage was then sent off with eight minutes remaining for a second yellow card for another late challenge on Rowe and despite some late pressure, Posh held on for a vital three points.