However Connacht had other ideas after the break scoring tries from Tiernan O'Halloran and Ethienne Reynecke while Leinster had Isaac Boss and Leo Cullen sinbinned.
However in contrast to Nacewa's efforts, poor form in front of the posts cost Connacht dear as missed penalties and both conversions saw them fall to a 12th straight defeat in all competitions.
Connacht dominated the early exchanges but had neither a try nor a penalty to show for their efforts with Matthew Jarvis particularly wasteful in front of the posts.
Jarvis first sent a fifth-minute penalty wide then missed a second moments later however he did make it third time lucky and opened the scoring shortly after.
He sunk a penalty from just outside the 22 to give Connacht a 3-0 lead and, while it took time for Jarvis to find his kicking boots, Nacewa wasted little for Leinster.
The New Zealand born full-back pulled Leinster level on the 12th minute with a penalty of his own and then put them ahead moments later with an almost exact effort.
And Nacewa completed a good half for Leinster in the 34th minute - slotting a perfect penalty, his third of the game so far, against a strong wind.
Nacewa picked up where he left off after the restart with a fourth successive penalty, this time the strong gale with him, to extend Leinster's lead to nine points.
Just as Connacht heads started to drop they were presented with a perfect opportunity to get back into the game with 55 minutes on the clock.
Leinster scrum-half Boss was shown a yellow card for impeding opposite number Frank Murphy - and Connacht quickly made the most of the one man advantage.
O'Halloran sold Leinster's outside backs a dummy and stormed home for the first try of the game in the 58th minute but Jarvis couldn't convert.
Leinster maintained their composure pressing Connacht and earning a reward in the form of Nacewa's fifth penalty from five attempts moments later.
But no sooner were they back to full strength and Leinster were a man down again - Cullen this time going into the referee's bad books with a yellow card in the 70th minute.
Connacht responded immediately and scored their second try through Reynecke however Miah Nikora, taking over kicking duties from Jarvis, couldn't convert as they trailed 15-13.
That set up a frantic final few minutes culminating in a Nikora drop goal that fell agonisingly short as Leinster held on for a vital victory against their Irish rivals.
|Connacht Rugby Score Card|
|Leinster Rugby Score Card|