Connacht recovered from a four-point half-time deficit to beat Edinburgh in the Pro12 clash at the Sportsground.
A Roddy Grant try, converted by Carl Bezuidenhout, gave the visitors a 7-0 lead but Craig Ronaldson replied with a penalty before the interval.
Michael Swift nudged the Irish province in front with a try and a Dan Parks penalty increased the winning margin.
The result moves Connacht off the bottom of the table. with Edinburgh remaining in eighth position.
Connacht had won only one of their last dozen Pro12 matches, beating the Dragons at the Sportsground in December - and results have been particularly hard to come by for Pat Lam's men.
Following Grant's first try of the season, Ronaldson knocked the ball between the posts but the home fly-half then missed his next three place-kicks as Edinburgh led 7-3 at half-time.
But Swift, Connacht's most-capped player, plunged over in the 47th minute and Parks came off the bench to kick the clinching penalty.
The westerners were unable to capitalise on their early possession and it was the visitors who swept into a seventh-minute lead, with Grant driven over following a quick ruck recycle.
Nick De Luca's break up to the hosts' 22 did the initial damage and Grant had good support as he touched down from close range. South African newcomer Carl Bezuidenhout added the conversion.
Kieran Marmion threatened for Connacht before they opened their account midway through the half, winning a penalty at an Edinburgh scrum which Ronaldson stuck over.
Ronaldson pulled a difficult effort to the right and wide in the 24th minute, but should have done better when hitting the post on the half-hour mark and also missed to the left with two minutes remaining.
Edinburgh had the wind at their backs in the second period but it was Connacht who lifted the intensity and accuracy of their play on the resumption.
Eoin Griffin provided the momentum with a rare line break and Cornell du Preez's sin-binning, five metres out from the Edinburgh line, gave Connacht the impetus to take the lead.
The Scots' brave defence finally relented as second row Swift crossed near the posts after a series of pick and drives.
Ronaldson's kicking woes continued though as he hit the post with the conversion.
Bezuidenhout missed a 51st-minute penalty and, with the wind dying down and their error count rising, Edinburgh's frustrations only grew.
Connacht took control as the second half wore on, with man-of-the-match Ronan Loughney a prominent figure up front, and Parks' drilled penalty in the 68th minute was enough to settle the issue.
Connacht: Henshaw, Carr, E. Griffin, McSharry, O'Halloran, Ronaldson, Marmion, Buckley, Harris-Wright, Ah You, Kearney, Swift, Browne, Heenan, Muldoon.
Replacements: Heffernan, Loughney, Cooney, Muldowney, Naoupu, O'Donohoe, Parks, D. Leader.
Edinburgh: Cuthbert, Fife, De Luca, Strauss, Brown, Bezuidenhout, Hart, Blaauw, Hilterbrand, Nel, Gilchrist, van der Westhuizen, Coman, Grant, Du Preez.
Replacements: Ford, Allan, Cross, Atkins, Leonardi, Hidalgo-Clyne, Beard, Leonard.
Referee: Claudio Blessano (Italy)