Boro dominated throughout and almost took an early lead through Andy Bond, who saw his volley cleared off the line.
Chris Beardsley has struggled for goals this season and it showed as he miskicked inside the area after 25 minutes following Chris Whelpdale’s cutback.
The visitors were struggling to contain Stevenage’s right side and good work from Whelpdale and Tom Conlon led to another chance for Beardsley, who was denied by a last-ditch intervention by Danny Grainger.
Just before half time the irrepressible Whelpdale drew a great save from Mark Gillespie with a rasping drive from the edge of the box.
After a profligate first half Parrett eventually broke the deadlock a minute into the second as he finished clinically from the edge of the box for his fourth goal of the season, following Tom Pett’s pass.
Carlisle’s first chance finally arrived on the hour mark and they should have scored as Brad Potts blazed over after a great run and cross from Kyle Dempsey.
With 15 minutes remaining Pett almost added a second after he cut inside and unleashed a fierce strike that cannoned off the post.
Jason Kennedy went close for Carlisle late on, but Stevenage held on for a well deserved win.