The two teams had played out a high scoring draw in Dublin earlier in the season, but this was an uncompromising, highly physical encounter in which the Leinster defence came out on top.
"They got one over us at RDS and it's nice to come here and put one over them and get one back. There was a lot of attrition out there and it wasn't easy. We've got to rest up now before next week," said Heaslip.
"We got taught a lesson by Munster in terms of being first to the breakdown last week We know that quick ball wins games and we gave that to our back line and we caused some damage.
"But the Ospreys kept going and going and that game could have gone either way in the end. It is always tight between us and we won the war of attrition at the tail end of the first half and in the second.
"We're happy with the win but we've got a lot to work on for next week. We're a week by week team, and we don't look too far ahead, but it would be nice to get out of our Pool."
Heineken Man of the Match Sean O'Brien, who scored the game's only try, claimed it had taken last season's Amlin Challenge Cup champions until now to find their feet after so much change in the summer.
"With a new coaching staff and new players it takes a bit of time to gel, especially as we have some new systems. It has taken five or six games to get to where we are now," said O'Brien.
"Everyone gets very excited at Heineken Cup time. The Heineken Cup is something we want to win every year and after last year we are a little bit sore about certain things and we want to put that right.
"We said trust the systems tonight. We stuck to our task and it worked for us."