Ten minutes in, the Exiles counter attacked from a loose kick to set up a penalty chance which was converted by out-half Harry O'Reilly to give them a 3-0 lead.
Connacht pressurised for the next period, but in their frantic efforts to get on the scoreboard they forced a pass that was gratefully intercepted by the Exiles to allow winger Matt Killeen to score a well-taken converted try.
To their credit Connacht stuck with their game-plan and were rewarded with a forwards drive and a seven-pointer which got them off the mark for half-time - 10-7.
From the restart, Exiles back rowers Lorcan Dow and Charlie Greene drove deep into Connacht's 22 and cleverly used their greater numbers to put Killeen in for a second score in the corner. The difficult conversion was slotted.
Connacht's response was swift and they produced a try which brought them back to within striking distance on a 17-12 scoreline.
Almost immediately the Exiles responded with a deep drive into Connacht territory where the Exiles scrum half Jack Cullen gratefully accepted a scrum turnover to intelligently unleash his backs to score a beautiful try and push the score to 22-12.
With time running out Connacht's efforts were eventually rewarded when a series of recycles allowed centre Sean O'Hagan, an Exile who has been at Connacht on a summer programme, to stretch out and bring Connacht to within a score on 22-17.
Connacht continued to look for the winning score, but the Exiles' defence held firm to give then the spoils in a match of high standard.
Next up, the Exiles Under-18s played Munster aat Thomond Park on Saturday, September 1. This match produced a game of a very high standard that was in keeping with the great venue.
The Exiles started as they had left off the previous week against Connacht and moved the ball at every opportunity.
This lead to early Exiles tries and only a few errors let Munster back into the game. In true Munster fashion they gained confidence from their scores and raced into a 28-14 lead.
The Exiles, to their credit, hung in there and pulled to within two points to set up an exciting last few minutes. With both sides playing great rugby, a final superb attack by the Exiles led to a match-winning try and although Munster looked like they may score in the final play, some resolute defence help the Exiles hold on for an historic win.
The Exiles Under-19s got their season underway against Connacht at the Sportsground on Sunday, September 9.
After the U-18 results, this turned out to be something of an anti-climax as the Exiles registered a disappointing 17-6 loss.
Connacht trailed 6-0 after conceding two penalties in the first 15 minutes, both of which were converted by Exiles out-half Sean O'Hagan.
The Exiles created plenty of opportunities but some poor decision making let the chances slip away and with Connacht working tirelessly in disrupting the breakdown, the Exiles struggled to keep a foothold in the game.
Connacht scored their first penalty after 25 minutes, punishing the Exiles indiscipline. The score at half-time was 6-3 to the Exiles but not long after the restart Connacht scored a try following a well-rehearsed move off a five-metre scrum, which was converted for a 10-6 home lead.
The Exiles pushed hard to find a winning score but with a few minutes left in the game, Connacht scored from another five-metre scrum through quick thinking.
They reacted well to a loose ball to put one of their centres in at the corner. The touchline conversion was added to leave the final score 17-6 to Connacht. The Exiles will look to improve on their performance going into next week's game against Leinster.