Polish hitman Grzegorz opened his account for Clive Allen's men in this comfortable win at Havant & Waterlooville FC with another double from Lee putting the issue beyond doubt with the scoreline reading 3-0 at the break.
It means 'Barney' has six goals in his last three reserves games - all doubles - and 10 in 11 games in the FA Premier Reserve League South this season.
On a particularly fresh evening in Hampshire, both Martin Jol and Joe Jordan mingled with the fans over a cup of tea ahead of kick-off in a game where Clive Allen was again able to field a side with considerable first team experience. Portsmouth, by contrast, featured only two players who have sampled Premiership fare this term - possibly reflected by the fact there appeared to be more Spurs people in attendance than Pompey.
Wayne Routledge set the game off in a positive fashion and forced Andrea Guatelli into a scrambling save within the first couple of minutes and somehow denied Barnard adding another to his goal tally from the rebound.
Routledge was looking waspish in the early exchanges, floating around and cutting in from the right flank, always seeking to apply a sting. But it was a Stephen Kelly cross from the right that led to the next opportunity, with Guatelli saving well from a Rasiak header.
The deadlock, such as it was, was broken on 13 minutes when a deep Jamie O'Hara cross from the right was met by a leaping Rasiak, whose header was planted wide of Guatelli and into the bottom left hand corner of the net. Rasiak again extended the goalkeeper seven minutes later but this time the ball was tipped over the bar.
The game drifted slightly until the 36th minute when Barnard seized possession some 20 yards out. A pass to Rasiak was the simple option, but the leading scorer with defenders close by, took the ball back and around before shooting low into the bottom right hand corner.
O'Hara nearly made it three following smart work down the left from Hallfredsson, but this time Guatelli was able to block the midfielder's instinctive volley. There was then a little scare when Routledge was sent flying in a crunching challenge from Matthew Day but, happily, he was able to continue and the defender was yellow carded.
Tommy Forecast was tested for the first time three minutes before the break when he athletically tipped away Kyle Swanyne's effort that looked bound for the top corner
It was a brief respite for Pompey because, on 44 minutes, Barnard netted his second with a nodded header past Guatelli from a Rasiak cross to make it 3-0 ahead of the interval.
The second half began with Pompey again rocked back on their heels with Rasiak teeing up O'Hara for an effort that did not miss the top corner by much. Twice more Rasiak made Guatelli work as Clive's side continued to ping the ball around with great conviction.
Goran Bunjevcevic completed a hour of his comeback match after recovering from a foot fracture and looked his usual unruffled self operating down the left flank. He was replaced by Charlie Daniels, who was responsible for the next best chance on 70 minutes when - after a lung-busting run - he drilled in a low shot across Guatelli from 20 yards that flashed just wide.
Pompey nearly snatched a replay with ten minutes remaining when Franck Songo'o found himself through on goal and hit in a decent thump of a shot that Forecast saved well down to his right.
Rasiak should have got another when Kelly presented him with the ball right in front of goal, but he failed to test the goalkeeper just after he denied Barnard his hat-trick with a save from a close-range header.
Routledge nearly rounded off the evening in style after solo run, but Clive will be more than happy with three goals and another three points.
Team: Forecast, Kelly, Bunjevcevic (Daniels 60), Lee, Gardner, Routledge, O'Hara, Davis, Hallfredsson (Barcham 73), Rasiak, Barnard. Subs: Button (GK), Mills, Lewis, Daniels.
Pompey: Guatelli, Day (McClory-Cuthbertson 44), Donaghey (Bye 74), Wilson, Silk, Pearce, Songo'o, Fordyce, Mbesuma, Swayne (Cousins 67), Compton. Subs: Harris (GK), Carter-Harris.
Grzegorz Rasiak netted his first goal as our reserves beat Portsmouth 3-0 on Tuesday night - but Lee Barnard grabbed the goalscoring headlines again.