After much debate, the rule book was consulted by officials before the five minutes each way extra-time got underway with the first team to score a point winning the game.
In the end it was Ulster by virtue of outscoring Leinster by three tries to two after the teams failed to register a point in the extra-time period.
It was two contrasting halves with Leinster storming into a 20-7 lead before Ulster completely ran the show in the second period to slowly claw back the deficit and eventually take the lead before Matthew Leek levelled in the sixth minute of injury time.
There was an explosive start for Leinster when they countered deep from their own half in the third minute after Shane Stewart had spilled a pass from scrum-half Kieran Campbell.
David Quinlan picked up the ball, fed winger Brian Burke whose kick and chase bounced kindly into the hands of Brown, who crashed over at the posts for Leek to convert.
It took a ragged Ulster side 15 minutes to settle, but they gifted Leinster a second try in their first real sortie upfield.
Scott Young looked to be impeded as he kicked through in a charge to the posts, but referee Nigel Owen allowed play to continue. Gordon D’Arcy collected and hoofed the ball downfield, but in attempting a chip out of danger, Adam Larkin saw his kick charged down and collected by scrum-half Brian O’Riordan, who had a simple run-in to the posts.
With Leek converting, Leinster surged into a 17-0 lead in as many minutes. Ulster, however, were not prepared to lie down and they began to turn the screw and in their efforts to stop the home side, Leinster saw their skipper Leon Cullen yellow-carded in the 28th minute.
From a resulting five-metre scrum, Leinster were punished when they attempted to prevent a pushover and the referee had no option but to award a penalty try, which Larkin converted.
Leek, however, responded quickly when Leinster meandered upfield and he converted his second penalty from in front of the posts.
Two Larkin penalties immediately on the restart brought Ulster to within a converted try of their opponents. Skipper Ward almost provided that score when he collected a wayward Leinster line-out to charge over the try-line, but was unable to ground the ball.
It as all Ulster in the second period, but the Leinster defence was proving extremely resolute, although when Ben Gissing was sent to the sin-bin after skullduggery at a ruck in the 54th minute, the game turned on its head.
A minute later, Ulster picked up their second try when they surged over from a line-out with flanker Neil Best touching down. Larkin missed the conversion, but Ulster stormed ahead for the first time in the 59th minute when Ward turned over possession and Campbell put a delicate kick into the corner for Tyrone Howe to outpace the defence to touch down with inches to spare.
Leinster then temporarily got out of jail in injury-time, but it was never going to be their night.
Scorers for Ulster : Tries: penalty, Best, Ward; Cons: Larkin, Pens: Larkin 2
ULSTER: B Cunningham; S Young, R Constable, S Stewart, T Howe; A Larkin, K Campbell; R McCormack, P Shields, B Young, M Mustchin, M McCullough, A
Ward, N Best, T McWhirter.
Replacements: J Topping for Young (56), S Mallon for Stewart (80), R Frost for Mustchin (56), S Shawe for Young (80), R Wilson for McWhirter (40).
Scorers for Leinster: Tries: Brown, O'Riordan, Pens: Leek 2, Cons: Leek 2.
LEINSTER: G D'Arcy; J McWeeney; G Brown, D Quinlan, B Burke; M Leek, B
O'Riordan; J Lyne, G Hickie, E Byrne, L Cullen, capt, B Gissing, A
McCullen, S Jennings, D Dillon.
Replacements: P Coyle for Lyne (40), A Kearney for Gissing (64), N
Breslin for Dillon (62), B O'Meara for O'Riordan (63), J Norton for
Referee: Nigel Owens (WRU).