Borough went ahead in the ninth minute through Robin Shroot, who tapped in while unmarked at the far post from Chris Beardsley’s low cross.
The visitors doubled their lead in the 25th minute when Don Cowen’s sharp turn allowed Beardsley to plant a low 25-yard shot past home goalkeeper Ben Williams.
Colchester midfielder Andrew Bond hit the woodwork and forced Borough goalkeeper Chris Day into a good save, before the U’s reduced the deficit six minutes after half-time when Ian Henderson headed in Karl Duguid’s deep cross from close range.
But Stevenage restored their two-goal advantage just after the hour mark through Michael Bostwick’s 30-yard effort.
Scott Laird then cleverly clipped in from Bostwick’s short free-kick for the visitors’ fourth and substitute Luke Freeman blasted in from close range, before Joel Byrom rounded off Stevenage’s emphatic win after bursting into the penalty area and firing past Williams with seven minutes to go.