Against a Connacht side who were determined not to simply make up the numbers the Welsh side were largely kept at bay in the first half.
However after first-half scores from Eli Walker and Justin Tipuric had helped them to a 12-6 half-time lead, they took control in the second half.
Jonathan Thomas' try immediately after the break helped the Ospreys move decisively clear and then, as they looked like they might miss out on the maximum points, Fotuali'i went over for the fourth try.
It took a quarter of an hour for the Ospreys to make the initial breakthrough, Walker getting on the end of some good patient buildup play before taking the scoring pass from Richard Fussell. Dan Biggar converted to stretch the lead to 7-0.
Connacht were determined to put pressure on their hosts though and two penalties from Dan Parks brought them back to within a single point five minutes before the break.
But the hosts scored again with Fussell playing a key role, stepping out of a couple of tackles, and sending Tipuric away out wide where the Welsh international finished in style.
The home side were in the ascendancy and added a third try straight after the break when Thomas reacted well to intercept a Parks pass and sprint over.
That appeared to take the wind out of Connacht sails but Parks added a third penalty to reduce the deficit to 19-9 after 52 minutes.
Biggar and Parks then both missed shots at goal as neither side was able to take control.
However with eight minutes remaining Fotuali'i spotted a gap in the Connacht defence off the back of a scrum and darted over to seal the maximum points for the home side.
It marked a fourth straight RaboDirect PRO12 success for the Ospreys, with Connacht in contrast having now lost their last two in the league.
|Ospreys Score Card|
|Connacht Rugby Score Card|