A try from scrum half David Moore in the fifth minute got the hosts off to a great start but Garryowen were right back in the contest after two fine penalties from Conor Murray.
However, 'Rock were well in front at the end of the first half, leading 24-11 through tries from hooker Cian Culleton and winger Kyle Tonetti.
Garryowen got off to a good start in the second half threatening the 'Rock try-line, but all they could muster was three points through another penalty from Murray.
The 'Rock back-line then seized control of the second period as both Andrew Conway and Brendan Macken were allowed to take advantage of a sluggish Garryowen defence and score a try apiece.
"We had great performances from Conway and Macken today," Blackrock coach Barry Gibney told IrishRugby.ie.
"These guys have a great influence on the team, they're coming through the Leinster Academy and playing club rugby and they're playing to a high level."
However, Gibney also gave credit to the forwards who provided great service for the back-line all afternoon.
"You have to look at where the platform came from. The pack was good and supplied good ball off set piece and phase play.
"Overall, the scoreline reflects quite a big performance. When you break it down, I thought when we got on top and got quick ruck ball, we were able to use our back-line and create opportunities and build a score from them."
Gibney was quick not to get carried away as he is fully aware of the challenges of the newly structured AIB League Division 1A.
"Obviously, when you put up a score like that you're going to be happy but the great thing about this league is that we have to travel down to Limerick later in the season and they will get a second shot at it."
Garryowen came into the match on the back of a dramatic 12-10 victory over defending champions Shannon last week when out-half Willie Staunton slotted a 45-metre drop goal to clinch the win.
But the tide quickly changed for them at Stradbrook as 'Rock put in a stunning performance to claim a bonus point victory.
Head coach Paul Cunningham expressed his disappointment at the result but conceded that his team were well beaten.
"I'm disappointed of course. We were well beaten by a very good side," he said.
"In fairness, 'Rock took every chance they got in the match. I thought we had opportunities at the start of the second half but they showed that they're a very good side, which we expected them to be.
"We trained well all week but it's just the nature of this league, you don't get a chance to breathe. The quality is there all the time."
The result may come as an early setback to Cunningham's charges but he remained optimistic about the next encounter with the Dublin side.
"It's one of those things, you get back on the bike straight away. We'll go back to train hard and fix the things we didn't do well today.
"We meet 'Rock again later in the season in Limerick and we'll see what happens then."