Victory lifted Alexander's side up to fourth in the table, three points adrift of an automatic promotion place.
Alexander said: "We had to make sure we got three points to make the draws we've been picking up recently worth it.
"We created chances and took them, which hasn't always been the case recently.
"We got the penalty which was long overdue.
"We know we're capable of good play, we've got players who can score goals.
"We're now in a good position coming into the business end of the season."
Jed Wallace did end Portsmouth's three-game goal drought but it was not enough to deny Fleetwood.
The home side's opener came from a throw on the right, Jamille Matt getting ahead of the Pompey defence and although his shot was saved by Trevor Carson, Jon Parkin was well placed to stroke home the rebound.
The lead was doubled 10 minutes later. Steven Schumacher swung over a cross and after Daniel Alfei was adjudged to have pushed Josh Morris, Antoni Sarcevic fired his spot kick straight down the middle.
Charlie Taylor could have extended the home side's lead 10 minutes after the break, but was denied by Carson after racing clear.
But the respite for Pompey was short-lived. Matt took advantage of confusion in a crowded box to stab home Fleetwood's third after another set-piece.
Pompey were not sunk however, and hit back in spectacular fashion through substitute Jed Wallace, whose dazzling run was crowned with a stinging shot to end the club's three-game goal drought.
But it was not enough to spark a fightback as Fleetwood substitute Mikael Mandron had a chance to make it four for Fleetwood, but his shot was blocked.