The home side went to the break 22-10 ahead with the Irish points coming via a Conor McKeon try and the boot of Conor Fitzgerald.
Gerard Ellis, a brace from Rosser, and Chris Coleman had given the Dragons a comfortable interval lead and the scoring intensified after the break.
Connacht came roaring back through Fitzgerald, Colm de Buitlear and Sean O’Brien added a brace.
But in a pulsating tie it was not enough as the outstanding Rosser scored three more of his own and Carwyn Penny and Calvin Wellington completed a home success.
The home side started the brightest, Ellis charging down a clearance and running in for a rare try which McKeon responded to almost immediately. Conor Fitzgerald converted.
De Buitlear then had a try ruled out for a forward pass, but Dragons seemed to take control as two quick scores from Rosser and an effort from Coleman put them ahead.
Will Talbot-Davies was only able to add one conversion from those four tries which left the door open for a Connacht comeback and so it proved.
The visitors started the second-half much the stronger side and began to assert their authority on proceedings, running in three unanswered tries through Fitzgerald, De Buitlear and O’Brien and three inch-perfect kicks from Fitzgerald made sure Connacht took maximum points.
The Irish raiders were strong in possession and despite occasional lapses in concentration which lead to some mistakes, their passing play was very easy on the eye at times and Dragons struggled to find an answer to it.
Connacht had the better of the possession as well as the territory, but out of nowhere the Dragons came back fighting with Rosser the leading light.
He added a second-half hat-trick to his brace in the first period and the best of his five tries came when he skipped through the defence before running in under the posts in the first half.
Rosser was simply too good for the Connacht defence as he staked his claim for a call-up to Bernard Jackman’s senior side and with his scores, plus those from Penny and Wellington, the Dragons came out on top despite another effort from O’Brien.
This was the perfect advertisement for the new Celtic Cup format. The pace did not let up from start to finish and the crowd at Ystrad Mynach were treated to a glut of tries, but there was no doubt it was Rosser who was the special talent on display.
Dragons A: Carwyn Penny; Will Talbot-Davies, Connor Edwards (Babos 8), Tiaan Loots (Wellington 55) ; Jared Rosser, Jacob Botica, Dafydd Buckland; Gerard Ellis, Rhys Lawrence, Chris Coleman, Joe Davies, Huw Taylor, Lennon Greggains, James Benjamin, Taine Basham
Replacements not used: Zac Hewlett, Scott Evans, Luke Yendle, Max Williams, Ben Fry, Deon Smith
Connacht Eagles: Darragh Leader; Rory Scholes (Conor Hayes 30), Sean O'Brien, Kieran Joyce, Colm de Buitlear; Conor Fitzgerald, Conor McKeon (James Mitchell 40); Matthew Burke, Tom McCartney (capt) (Jonny Murphy 62), Conor Carey (Conor Kenny 66), Peter Claffey, Joe Maksymiw, Cillian Gallagher, Cian Huxford, Robin Copeland (Neal Moylett 40)
Replacements not used: Jordan Duggan, Cormac Daly, Conor Dean
Referee: Elgan Williams (WRU)