Boro, who thrashed Sheffield Wednesday 5-1 at the Lamex Stadium in midweek, succumbed to goals either side of half-time from Lee Hughes and Ben Burgess.
Graham Westley's side had a great chance to take an early lead, only for Craig Reid to miss a sixth-minute penalty. Krystian Pearce hauled down Reid in the box, but the young forward saw his spot-kick beaten away by Stuart Nelson.
Darius Charles also went close for the hosts before Notts responded with a crisp drive from Neal Bishop which Chris Day saved well.
The Magpies took the lead in first-half stoppage time. Mike Edwards crossed for veteran striker Hughes, who made no mistake from close range. Just five minutes after the restart Martin Allen's men doubled their advantage when Burgess headed home Jeff Hughes' cross.
Substitute Josh Walker had a late chance to grab a late consolation for Stevenage but he fired wide.