Edinburgh outscored Connacht by three tries to two in the RaboDirect PRO12 as they picked up just their second away victory since January.
Tim Visser, Matt Scott and Stuart McInally all crossed for the Scottish side in Galway, with Willie Faloon and Danie Poolman touching down for the hosts.
Greig Laidlaw provided the assists for the Scott and McInally tries, in addition to his kicking haul of three conversions and a penalty, as Edinburgh edged the contest 24-23.
Former Scotland outside-half Dan Parks, who finished with 13 points, had a late chance to win it for Connacht but his drop-goal effort shaved the right-hand post.
- Sports & Recreation
- Willie Faloon
- Stuart McInally
- Tim Visser
- Danie Poolman