After the opening exchanges the only scores registered was a penalty a-piece for Lolo Lui and Connacht's Miah Nikora.
Flanker Timoteo scored the opening try of the evening for the visitors, rounding off a slick attack and Lui added the two points with the conversion.
Nikora then replied by kicking two more penalties to bring the scores to within a single point.
Samoan openside, Selesele then took advantage of some slack Connacht defending and went under the posts to score, Lui adding the extras.
Just before the break Connacht got the try the deserved as their backs came to life. Eoin Griffin and Troy Nathan combined to put Brian Touhy in under the posts. Nikora added the conversion to bring the half-time score to Connacht 16-17 Samoa.
Connacht took the lead for the first time three minutes into the second half, Nikora on form again, slotting another penalty.
Samoa scored their third try as they showed their international class, touching down in the corner. Lui missed the conversion, just as he had with a penalty moments before the try.
A powerful scrum was rewarded as John Muldoon crossed for Connacht and Nikora kicked the conversion from out wide to give the Irish province an historic victory.