Ulster returned to the victory trail, in the PRO12, after claiming a 22-18 victory over Leinster in Dublin on Saturday.
The win moves Ulster into second position in the standings and ended Leinster's winning streak in the league.
It was the boot of Ian Madigan which separated the sides at the break as his four penalties took the hosts 12-8 ahead, with the visitors' response coming through Robbie Diack's try and Ruan Pienaar's penalty.
Madigan added two more three-pointers in the second half but Iain Henderson's touchdown and nine more points from Pienaar sealed a courageous win.
Despite one point separating these two teams going into the encounter, their respective forms were vastly different.
The Dubliners went into the game having won seven in a row in the PRO12 while the Northern Irish province had secured just a single victory in five league matches.
However, the Ulstermen had several players returning from injury and they started brightly, putting pressure on their opponent's defence.
But it was the hosts who took their opportunities early on when Madigan kicked successive penalties to take them into a 6-0 lead.
Although the visitors immediately responded with a try from Diack, after an excellent burst by Nick Williams, a third three-pointer via the boot of Leinster's fly-half took them 9-5 ahead.
Madigan and Pienaar then traded kicks from the tee as Joe Schmidt's men took a 12-8 advantage into the interval.
The home side's stand-off was again successful via the boot, but a pair of penalties from Ulster's scrum-half reduced the deficit to one point after 57 minutes.
And they shocked the majority of the RDS crowd when Henderson touched down after an excellent period of play which saw the ball moved through several phases.
Although Madigan kicked his sixth three-pointer Pienaar's long-range effort secured the victory, despite a late Leinster onslaught.
Pens: Madigan 6
Tries: Diack, Henderson
Pens: Pienaar 4
Yellow card: Payne (80th minute)
Leinster: 15 Rob Kearney, 14 Dave Kearney, 13 Brendan Macken, 12 Gordon D'Arcy, 11 Isa Nacewa, 10 Ian Madigan, 9 Isaac Boss, 8 Jamie Heaslip (c), 7 Shane Jennings, 6 Kevin McLaughlin, 5 Quinn Roux, 4 Devin Toner, 3 Mike Ross, 2 Richardt Strauss, 1 Cian Healy.
Replacements: 16 Sean Cronin, 17 Jack McGrath, 18 Jamie Hagan, 19 Leo Cullen, 20 Rhys Ruddock, 21 John Cooney, 22 Andrew Goodman, 23 Andrew Conway.
Ulster: 15 Jared Payne, 14 Andrew Trimble, 13 Darren Cave, 12 Stuart Olding, 11 Craig Gilroy, 10 Paddy Jackson, 9 Ruan Pienaar, 8 Nick Williams 7 Chris Henry, 6 Robbie Diack, 5 Dan Tuohy, 4 Johann Muller (c), 3 Ricky Lutton, 2 Rory Best, 1 Tom Court.
Replacements: 16 Rob Herring, 17 Calum Black, 18 Kyle McCall, 19 Lewis Stevenson, 20 Iain Henderson, 21 Roger Wilson , 22 Paul Marshall, 23 Peter Nelson.
Venue: Royal Dublin Society
Referee: George Clancy
Assistant referees: Leo Colgan, David Connolly