Head coach Cullen had made ten changes ahead of kick-off with Isa Nacewa the only back retained and the skipper repaid that faith with 14 points from the boot.
Leinster led 9-6 at half-time as Nacewa and Craig Ronaldson exchanged penalties while Sean O'Brien and Peter Robb both saw yellow cards.
Despite both teams being down to 14 men for a time, it wasn't until the second half that either defence could be breached with Byrne finishing well in the corner.
Daly sealed the win, and a dream Leinster debut, late on and the result leaves Connacht, who had a consolation score from Shane Delahunt, eighth in the Guinness PRO12 with two wins from their opening six games.
And Cullen was delighted to see Leinster move to the top of the Guinness PRO12 table level on points with Ospreys and Glasgow Warriors.
"It was an important win, it keeps that bit of momentum going in the league," he said.
"It was a short turnaround as well from Montpellier into this week so we were limited in terms of what we could do preparation wise.
"These weeks are a really good opportunity for us to see new players. Guys are pushing hard, there's competition for places.
"We kind of expected that kind of disjointed nature but the effort and endeavour was very positive and guys in the squad are showing really good characteristics at the moment and that's pleasing.
"It's a great window because we are pushing deep into our Academy group and it's great to see them up close, we enjoy it as coaches."
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