Former Portimonense player Fabio Nunes set up the goal on his return to the Estadio Municipal, breaking clear on 14 minutes, before crossing for Best to slot home.
The victory was just reward for the Rovers players, who had worked hard all week in the searing heat.
It was also fitting that the goal should go to Best, who suffered a serious knee injury in a pre-season friendly exactly 12 months ago.
Earlier, Anselmo had struck the post, as the hosts had the better of the first half, while Simon Eastwood was called upon late on to preserve Rovers' clean sheet.
That's now a draw and a win for Rovers, as they step up their pre-season preparations ahead of the 2013-14 Championship campaign.
Bowyer named a similar starting line-up to the one that took to the field at Wrexham last weekend, with captain Scott Dann, Ruben Rochina and Jason Lowe all getting their first run-outs of pre-season.
Josh Morris, who was the fourth new addition to the side, set up the first chance on nine minutes. The full-back played the ball through to Best, who hurdled the challenge of the onrushing keeper, but was forced too far wide to threaten the unguarded goal.
Staight up the opposite end, the lively Diego Souza delivered a low cross from the right into Anselmo, who got infront of his marker and flicked the ball goalwards, but his shot bounced back off the up-right. Jake Kean may have made a fine fingertip save.
Rovers then opened the scoring with a well-worked break. Nunes burst clear down the left and unselfishly centred the ball to Best, who tapped home at the far post.
Alan Judge fired an ambitious volley well wide on 27 minutes, before the home side started to gain the upper hand.
On the half-hour mark, Ricardo Pessoa delivered a corner from the right, Rui Correia's free header was blocked and so was his follow-up.
On 37 minutes, another Pessoa corner from the right was met by Souza, but his header was deflected over.
Moments later, a third Pessoa corner from the right found Souza, who got up above Grant Hanley, but his towering header was claimed by Kean.
On the stroke of half-time, following a foul by Jason Lowe on Souza, Ze Miguel's 25-yard free-kick had to be tipped over the bar by the Rovers keeper.
Rovers made 10 changes at the break, with trialist Yann Songo'o the only survivor from the first half and Matt Kilgallon making his Rovers bow.
The second half took a while to get going, with Portimonense registering the first effort of note on 59 minutes. Pessoa floated in a free-kick from the right and Andre's header was comfortable for Simon Eastwood.
Alex Marrow made his Rovers return midway through the half, replacing Josh King.
On 76 minutes, substitute Joao Nascimento tried his luck from long range, but Eastwood got his body behind it.
Two minutes later, Markus Olsson got to the byline down the left and his near-post cross found Jordan Rhodes, who had two bites of the cherry, but he just couldn't force the ball home.
Portimonense almost snatched an unlikely equaliser on 85 minutes when Souza played in Nelsinho one-on-one with Eastwood, but the Rovers keeper made a superb save.
As the final whistle went, the entire Rovers squad headed over to the far side of the stadium to applaud the travelling fans, who had appreciated their efforts throughout.
The team returns home tomorrow, before continuing their busy summer schedule against Crewe on Tuesday night.
Portimonense: Ramos, Moreno, Pessoa, Miguel, Gonzalez, Souza, Anselmo (Nascimento 63), Filipe, Zambujo, Nelsinho, Correia.
Rovers (1st half): Kean, Songo'o, Hanley, Dann, Morris, Judge, Lowe, Pedersen, Nunes, Rochina, Best.
Rovers (2nd half): Eastwood, Orr, Songo'o, Kilgallon, Olsson, King (Marrow 69), Dunn (King 87), Taylor, Rosado, Campbell, Rhodes.