The sides were locked at 3-3 for over 50 minutes until Luke Fitzgerald made a telling break and laid off for Horgan to make the line despite the best efforts of Ian Dowling.
It was a forgettable night for Munster and in particular their stand-in captain Ronan O’Gara who missed three penalty kicks out of four attempts.
The game had been billed as the renewal of World Cup rivalries between O’Gara and Leinster’s Felipe Contepomi, who inspired Argentina to beat Ireland in Paris in September.
Munster struggled from the start as they spilt the kick-off and infringed at the first scrum, allowing Contepomi to kick the visitors in front from just outside the 22.
The errors continued to mount with Leinster’s Brian O’Driscoll and Cillian Willis both kicking out on the full.
O’Gara sent his opening kick of the night wide but in the 13th minute the Cork-born playmaker levelled with a great strike from 49 metres.
Both sides kicked regularly to press the opposition into mistakes, but players like Shaun Payne and Rob Kearney showed their coolness under high balls.
Leinster’s pack built up a head of steam midway through the half and they should have crossed the whitewash. Only some disciplined defence and excellent counter-rucking from Munster kept the out.
Lifeimi Mafi and O’Gara led a Munster surge into the Leinster 22 but it came to nothing and Leinster got close to the home line again before the break.
Malcolm O’Kelly claimed a lineout and his team-mates mounted a big drive, Gordon D’Arcy weaved his way past four men but possession was frustratingly turned over.
Leinster also lost captain Brian O’Driscoll to a leg injury after half an hour, meaning Jonathan Sexton came in at number 10 and Contepomi moved to centre.
Munster looked poised to take advantage when they started the second half with some of the verve which saw them hammer the Dragons at the same venue last week.
Yet they failed to turn their pressure into points with O’Gara missing two place kicks after 45 and 64 minutes, while Contepomi also missed the target in the tricky conditions.
The game's turning point came soon after O’Gara’s third miss.
Young winger Fitzgerald caught the Munster defence napping with a fantastic burst forward, he stood up in the tackle and passed for centre Horgan to charge forward and use his momentum to crash over.
Contepomi brilliantly swung over the conversion for a 10-3 lead and Leinster’s stubborn defence allowed them to hold on for their third impressive away victory of the league campaign.