Marc McNulty and Kal Naismith gave Paul Cook’s side a 2-0 win at the Lamex Stadium.
That saw the Blues close the gap to the automatic promotion places - with nine points now the gap with 12 games to go.
And it also gave Pompey their first clean sheet since the start of January.
It wasn’t always pretty on a heavy pitch and with the rain pouring down through the second half, but Cook’s men deserved the three points.
It took two minute for Ben Davies to whip in an inviting cross but no blue shirt was there to tap the ball home.
Keeper Jamie Jones saw two crosses fly past his head in quick succession after 13 minutes but again no Pompey player could apply the final touch.
The lively Gary Roberts then tried his luck from 25 yards but Jones gathered.
Stevenage had a good chance after 18 minutes but Michael Tonge acrobatically volleyed just over from six yards.
Pompey made the breakthrough three minutes later, and it was all about the endeavour and quality of Roberts.
The attacking talent mugged the ball away from Lee Cox 45 yards out and threaded a perfect ball through to Marc McNulty who confidently slotted it away.
Stevenage replied with Tom Conlon heading over from Ronnie Henry’s cross.
Pompey broke four on four moments before the break but Evans cracked his shot wide from the apex of the box.
Fulton was required to tip over Conlon’s 25 yarder five minutes after the restart.
Then Jones was equal to Roberts’ shot at the near post seven minutes later.
Captain Michael Doyle saw his 25 yarder tipped over by Jones as Pompey pushed forward.
But there was a stroke of luck for the Blues at the other end as Tom Pett’s shot appeared to be on his way until it hit Byron Harrison.
Luke Wilkinson then impressively blocked Evans’ shot with it on its way after 65 minutes.
Michael Smith and Kal Naismith replaced McNulty and Roberts with 20 minutes left.
There was a let off with 10 minutes left when the ball rolled free in the box but Connor Ogilvie shanked his shot over.
Seconds later it was 2-0 as Bennett put the ball into Naismith’s pass and he thumped home emphatically from 10 yards out.
That made it a comfortable finale, althoigh Conlon did crack a 30 yarder off the bar in stoppage-time.