TheÂ 113-run success gave Jack Marston's fourth-placed side their seventh successive victory.
And the skipper has challenged his team to keep their winning run going in pursuit of runners-up spot.
'˜Leaders Bournemouth are probably too far ahead to catch because they keep winning,'Â said Marston.
'˜But I don't see any reason why we can't overhaul Calmore and Sarisbury.
'˜We beat CalmoreÂ in what was probably our biggest test so far this season.
'˜Sarisbury at their place is next up and that is a big game for both teams.
'˜The important thing is to keep applying ourselves because the league is so tight.
'˜OTsÂ are only 30 points behind us and they are in the relegation zone
'˜Any team between fourth and 10th can still end up being relegated.
'˜We must keep looking up rather than down, though.'
Middle-order batsman James Christian laid the foundations for the win.
He scored 65 off 98 balls, including seven fours,Â at a time when Portsmouth looked they might collapse.
In the end, Christian guided them to 250 for nine.
Earlier Ben Duggan and Jordan Palmer-Goddard had given the hosts a steady start.
Fraser Hay (54 off 51 balls) carried itÂ on but suddenly Portsmouth started to lose wickets.
'˜We had a little wobble when we lost two or three wickets very quickly,' added Marston.
'˜James, however, then provided the glue for our innings.
'˜He was patient and towards the end he was able to accelerate nicely.'
Calmore made a reasonable start to their reply but good bowling from the hosts meant the required rate soon climbed.
Hay (three for 15), Vikram Dawson and Fahad Ahmad kept it tight.
And whenÂ Calmore began chasing the game, left-arm spinner Andrew Marston (four for 34) put paid to their hopes.