Murray Houston's side claimed their historic win through match in which the team played with skill, grit and control.
The team started the match fully on the front foot, as they hoped to beat a Connacht side who had beaten them last weekend at the Sportsground Stadium in a tight 29-24 contest.
The feeling was that Ulster could have closed out a win on another day, and the team went into this Play-Off knowing that they could hurt their opponents.
Ulster started on the front foot, with scrum half Rachael McIlroy scoring an early try, after an offload from India Daley that was good reward for the fast start made by the team. Ella Durkan kicked two extra points to send Ulster into a 7 point lead.
Connacht attempted to battle their way back into the match, but were halted by a stubborn rearguard, Ulster showing great defence to hold up a try attempt on the 15 minute mark.
Ulster were getting joy in the breakdown and had good control in the game, with the positve momentum resulting in a second try- through the powerful India Daley, who managed to ground the ball despite Connacht pressure on the line. Ella nailed her second conversion of the match.
It was clear to see that India, Brittany Hogan and Maebh Clenaghan were all causing Connacht problems with their impressive ball-carrying and pushing Ulster up the pitch.
After the second try, Ulster's defence held out strong as they battled to half-time, even with a player down after Taryn Schutzler was sin-binned for an offence.
A positive first half as Ulster went into the dressing room in the lead.
HT: 0-14
Ulster knew a fast start in the second half was important as they aimed to close out a win.
The impressive Ella Durkan got the province off to a dream start, as she capitalised on a sluggish pass to sprint clear down the wing for Ulster's third try. She unfortunately couldn't add the icing on the cake as her conversion sailed wide.
Connacht replied soon after with a try from Lily Brady which was converted by Nicole Fowley.
Not intent on sitting back, captain Beth Cregan, showed great determination to power over the line for Ulster's fourth try, crashing over after a lineout maul. It was the captain's second try in successive weeks against the same opposition.
Ulster showed they could do both sides of the game well, with a big moment for the forward pack as they won an important scrum on the hour mark.
The positive momentum continued as the speedy, combative winger Niamh Marley produced a stunning line break to burst through Connacht and score for Ulster's fifth try. Ella made no mistake from the conversion to send Ulster into a 7-31 lead.
The defence got another pat on the back as they held up another Connacht try, showing their determination to stay sturdy in the defending.
It was clear to see in the celebration of the shutout that the players knew the importance of killing momentum.
Connacht were able to add a converted try before prop Aishling O'Connell killed the game off with a try at the death, following a well-executed lineout maul.
Ella Durkan's kick sailed wide but that didn't matter to the Ulster players who sank to their knees at the full-time whistle.
Those on Ulster's bench sprinted onto the pitch to soak in the win with the players still on the field.
It was clear to see the relief and pride etched over the faces of the players, who had achieved a first win in over a decade.
The players hugged each other as they celebrated a Play-Off win that was achieved with impressive determination and secured a long awaited win.
FT: 14-36
Player of the Match- Beth Cregan
Teams
Ulster:
(1-8) Ava Fannin, Beth Cregan, Aishling O'Connell, Keelin Brady, Taryn Schutzler, India Daley, Maebh Clenaghan, Brittany Hogan
(15-9) Ella Durkan, Maeve Liston, Peita McAlister, Kelly McCormill, Niamh Marley, Abby Moyles, Rachael McIlroy
Replacements: Sarah Roberts, Megan Simpson, Megan Brodie, Stacey Sloan, Brenda Barr, Laura Cairns, Toni Macartney, Megan Edwards
Connacht:
(1-8) Grainne O'Loughlin, Stacy Hanley, Nimah O'Grady, Sonia McDermott, Eva McCormack, Orla Fenton, Lily Brady Kayla Waldron
(15-9) Meabh Deely, Ava Ryder, Clara Barrett, Shannon Touhey, Laoise McGonagle, Nicole Fowley, Olivia Haverty
Replacements: Maria Kelleher, Niamh Corless, Dearbhla Canty, Mollie Starr, Faith Oviawe, Poppy Garvey, Orla Dixon, Cliodhna O'Sullivan