Nathan Elder's fine double kept Albion's hopes alive of securing the Pontin's Holidays Combination Central Division crown.
The burly striker, still awaiting his first senior start for the club since he was plucked from non-league Billericay in January, did his first team hopes no harm at all with an impressive performance against a youthful Bournemouth side.
Elder struck twice in the space of 90 second-half seconds - first with a powerful header and then moments later with a 25-yard rocket of a strike that gave Bournemouth goalkeeper Ryan Pryce no chance at all.
Albion director of football Martin Hinshelwood said: "He's come from non-league football and he has worked hard at his game. I think he has realised he had to work harder than he may have first thought but he took his goals very well - although he could have had four or five.
"Perhaps he hasn't done as well as he should have done since he joined us but he's proved again he can be a real handful and can score goals.
"It was a great header for the first one and then a cracker of a strike for his second. He also hit the bar but he's starting to realise what the game is all about now."
Although Brett Pitman pulled one back for the home side with a free-kick, it was Albion who looked far more likely to extend their lead in the latter stages and deservedly hung on for the victory.
If they can do the same again in the second part of the Bournemouth double-header at Worthing tomorrow (7.00), the title will be theirs.
Hinshelwood smiled: "Having worked at Portsmouth for four years it would be nice to pip Southampton!
"But these boys are a pleasure to work with and I think they deserve to win it."
After a decidedly uninspiring first 45 minutes of action, Elder at last offered some excitement when he rose to power home James Martin's corner nine minutes after the restart.
And he doubled the lead in the blink of an eye, winning possession deep in opposition territory before unleashing a superb drive that rifled into the bottom corner.
He should have completed at least a hat-trick, seeing one header rattle the crossbar and then heading over late on.
But his pace and strength were a problem for the home defence all evening and, with a constant quality supply from Alex Frutos down the left flank, it was too much for the Cherries to handle.
Albion Reserves: Kuipers, Hinshelwood, Cobbs, Fraser, Elphick, Pearson, Fogden (Skinner 46), Martin (Breach, 69), Elder (Gargan, 87), Gatting, Frutos. Subs not used: Sullivan, French.
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