The Hawks suffered more disappointment at Westleigh Park as Chelmsford City snatched a 1-1 draw in National League South.
Winning on home turf continues to prove difficult for Lee Bradbury’s men, who led through a first-half strike from Jason Prior.
They let victory slip from their grasp in stoppage-time, though, when Michael Spillane rescued a point for the Essex visitors.
The Hawks made one change to their starting line-up following the win at East Thurrock United, with Pompey loanee Theo Widdrington replacing Theo Lewis.
However, it was the Clarets who were on the front foot straight away and pressed the hosts back in the early stages.
Wes Fogden set up the first chance for the Hawks after 15 minutes, when he slipped Rory Williams through.
But Williams could only scuff his shot across the face of the Chelmsford goal from a good position.
Both sides struggled to fashion any clear-cut chances as they soon began to cancel each other out.
However, the Hawks finally struck the first blow when they took a 26th-minute lead.
Fogden picked up a poor clearance and laid the ball off to Prior and the striker’s low shot was deflected just inside the far post.
The Hawks began turning up the heat on their visitors on the stroke of half-time but could not add to their lead before the break.
Bradbury’s side started the second half in the ascendancy, too, as they forced a couple of corners in quick succession.
Williams made a tremendous burst forward down the left channel but overhit his cross with Prior lurking on the far side.
Widdrington then produced a lovely bit of skill to trick two defenders before drilling a 25-yard shot over the crossbar.
On 67 minutes, East Thurrock hero Alfie Rutherford replaced Widdrington as the Hawks looked for a second goal to kill the game off.
And it almost arrived 10 minutes from the end when a Williams corner flashed across the face of goal.
However, deep into stoppage-time the Hawks’ efforts were undone when Spillane fired an equaliser into the far corner after a free-kick fell to him in the area.
Hawks: Young, Strugnell, Williams, Woodford, Harris, Fogden, Prior, Tarbuck, Carter, Robinson, Widdrington. Subs: Lewis, Tubbs, Rutherford, Rose, Barker