Although he hails from the local area,Â Tuson-Firth had previouslyÂ been playing for Manley FC while living in Australia and with Aldershots under-23s.Â
The marksman gave the Royals a first-half lead with a header before Olly Searle doubled the hosts' advantage after the interval at the Crest Finance Stadium.
Lymington pulled a goal back but Tuson-Firth sealed the victory with a great 25-yard strike.
Mick Catlin was impressed with the forward's bow.
The Portchester boss said: 'GeorgeÂ looks a decent player and could prove a useful acquisition for us.
'˜This win keeps us up there and means we have closed the gap on Horndean.'
The fourth-placed Royals moved within two points of Horndean, who conceded in the 87thÂ minute to slip to a 1-0 defeat at Sholing.
Michael Birmingham felt his side were unlucky not to end the hosts'Â perfect league record.
'˜We came away feeling a little hard done by,' said the Deans boss.Â
'˜I am proud of the way we played and our bravery on the ball.
'˜Their goalkeeper pulled off four fantastic saves to keep us out.
'˜It was a good game with both teams going hammer and tongs at each other.
'˜We felt their lad was at least three yards offside for the winner.'
Meanwhile, Baffins Milton RoversÂ returned to winning ways with a comfortable 3-0 win against Bashley at the PMC Stadium.
Manager Steve Leigh felt it was good preparation for their big FA Vase tie at Bradford Town next weekend.
He said: '˜It was a good all-round performance both in attack and defence and I have to be pleased.
'˜Our movement was great and we produced three excellent finishes.
'˜The lads are full of confidence and playing some great football.
'˜We can go into our massive FA Vase game with no fear.'
Fareham TownÂ had to settle for a 2-2 draw against Christchurch at Cams Alders.
The Reds took a 23rd-minute lead against the run of play.
Simon Woods worked his way into the area and scored with a low shot that went in off the post.
The visitors, however, hit back to score twice before the break.
On 61 minutes the Reds were level again when Gary Moody tapped in from close range.
Home goalkeeper Declan McCarthy then pulled off three outstanding saves to earn his side a point.
In division one,Â a brace from Harry Potter and a Mig Dark effort earnedÂ United Services PortsmouthÂ a 3-2 win against East Cowes Vics at the Victory Stadium.
Jordan Neal poked homeÂ Petersfield Town'sÂ consolation goal in a 3-1 defeat at Romsey Town.