But Boro keeper Alan Julian pulled off two top-drawer saves to keep Carlisle at bay, although he had not chance of keeping out Chris Lumsdon's fierce 75th minute spot-kick.
Julian had denied Karl Hawley in the 20th minute with a diving save to tip the striker's 30-yard drive round his post, one-handed.
And Stevenage struck out of the blue, scoring with their first on target effort after 35 minutes.
Stamp had his back to goal when the ball was fed to his feet just inside the Carlisle box and his acrobatic overhead kick looped over rooted keeper Matt Glennon from 14 yards.
A howler by Glennon let Stamp in for his second virtually from the kick-off. Lumsdon hit an off-target back pass that the keeper raced out to rescue but, on a pitch partially covered by snow, he miscued his clearance straight to Stamp, who slotted the ball into an empty net.
Carlisle pushed three up front for the second half and sub Glenn Murray saw a close-range header palmed against the bar by Julian as Stevenage clung on to their two-goal cushion.
Then the keeper denied Murray with a tremendous 65th save - clawing away a 22-yard piledriver one-handed.
Carlisle were buoyed by a 79th minute penalty when Barry Laker brought down Magno Vieira on the by-line and Lumsdon made no mistake from the spot.
But despite their pressure, Carlisel couldn't find an equaliser.
Afterwards Cumbrians boss Paul Simpson, who has seen his side fail to win in their last eight league outings, said: "We showed great spirit in the second half, but you can't legislate for the mistakes we made in the first half."