The home side went close on 26 minutes when Allan Tait broke free down the inside left channel and squared to Robert Kember, who saw his side-footed effort hit the foot of the post before being scrambled clear.
The Cumbrians responded with an equally good opportunity two minutes later after Glenn Murray was sent clear on goal by a through ball from Paul Arnison.
The 18 year old, making his second start of the season, tried to dribble round keeper Phil Smith but the former Millwall stopper had read the danger and smothered the ball.
Crawley went close again five minutes after half time when Tait headed on to the crossbar from close range following a Charlie MacDonald cross.
That opportunity began a spell of pressure by the hosts which got its reward in the 67th minute.
Ryan Palmer floated a cross into the danger zone from the right wing and Armstrong arrived late to power home a header from 12 yards.