The home side got off to a strong start, with Finn Treacy running a good line to score in the tenth minute. Sean Naughton converted the try.
There was a quick response from Ulster, as winger Zac Ward produced a quality finish, being tackled short of the line but stretching out a hand to dot on the line. The unconverted try got Ulster off the mark.
Ulster had to defend hard against the physical Connacht side, with Lukas Kenny putting in a vital tackle on the Connacht hooker, McBurney, as he drove at the line, causing a knock-on and giving Ulster the scrum.
Connacht's pressure paid off and they scored a second, after a maul powered their forwards over from close range. Naughton's added conversion brought the scoreline to 14-5.
Captain Harry Sheridan showed his strength around the set piece with a vital lineout steal to relieve the pressure.
In a late flurry to the half, Ulster went to the corner and set up their own lineout maul attack. Blindside flanker, Tom Brigg, was able to peel off the back of the lineout maul and dive over the line for a superb score before HT. Aidan Morgan's conversion made it a two-point match at HT.
HT: 14-12
Shortly after the break, Connacht scored their third after an attack into the Ulster 22 down the left wing was recycled towards the middle of the field, and tighthead prop, Fiachna Barrett, powered over.
Naughton's conversion brought the scoreline to 21-12.
Ulster dug in at times and had to defend well with Connacht making more threatening attacks. An attack following a lineout maul was turned over close to the Ulster tryline, which would turn out to be a huge play.
19 year-old prop, Tyrese Abolarin, was sent on to make his first appearance at this level and was quickly thrown into some meaty prop work around the scrum.
Ulster kept showing grit and determination on both sides of the ball to get themselves within touching distance.
Replacement centre, Jonny Scott, showed good anticipation to intercept a Connacht pass out wide and the Academy man showcased his speed and strength to gallop into the Eagles 22 and fend off his defender to score in the corner.
The try went unconverted leaving the scoreline at 21-17 with minutes left in the contest.
Ulster were tenacious in their pressure around the breakdown and were piling the pressure on Eagles, who were conceding penalties giving Ulster momentum.
The match-winning moment came after Ulster stayed patient in possession while attacking into the Connacht 22. With smart passing from the backline Ethan Graham was fed wide in the left channel and he had the speed to run in the all-important try with the clock in the red.
Ulster's players, both on the field and on the sidelines all celebrated the late score, which was good reward for their tenacity in the second half, as at one stage the game could have gotten away from them. A well deserved late win for the Ulstermen in Galway.
Scorers
Connacht Eagles:
TRY: Treacy, Coghlan, Barrett
CON: Naughton x3
PEN:
Ulster 'A':
TRY: Ward, Brigg, Scott, Graham
CON: Morgan
PEN:
Teams
Connacht Eagles
1\. Temi Lasisi, 2. Adam McBurney, 3. Fiachna Barrett, 4. Joe Joyce, 5. Charlie Coghlan, 6. Niall Murray, 7. Charlie Keane, 8. Oisin McCormack, 9. Colm Reilly (C), 10. Sean Naughton, 11. Shane Mallon, 12. John Devine, 13. Finn Treacy, 14. James Nicholson, 15. Harry West
Replacements:
16\. Matthew Victory, 17. Jordan Duggan, 18. Thomas Connolly, 19. David O'Connor,
20\. Cian Brady, 21. Chay Mullins, 22. Shane Jennings
Ulster ‘A’
1\. Jack Boal, 2. James McCormick, 3. Bryan O’Connor, 4. Harry Sheridan (Capt), 5. Charlie Irvine, 6. Tom Brigg, 7. Reuben Crothers, 8. Lorcan McLoughlin, 9. David Shanahan, 10. Aidan Morgan, 11. Zac Ward, 12. Ben Carson, 13. Wilhelm De Klerk, 14. Lukas Kenny, 15. Rory Telfer
Replacements:
16\. Zac Solomon, 17. Tyrese Abolarin, 18. Cameron Doak, 19. Joe Hopes, 20. Josh Stevens, 21. Conor McKee, 22. James Humphreys, 23. Jonny Scott, 24. Ethan Graham, 25. Ben McFarlane.