Former Leinster fly-half Contepomi missed with a penalty attempt in the final minute of the half.
It means Ulster have still not won away to Leinster for over 10 years.
Following their 45-8 defeat to Leinster on Friday boss Nigel Davies said they must improve.
Rival New Zealand full-backs Blair and Leinster debutant Isa Nacewa scored a try apiece.
Leinster then piled on the pressure but were held up just short of the line.
The Connacht forwards produced an electrifying finale but the 14 men of Leinster hung on.
Leinster managed a consolation Simon Keogh try on 78 minutes, about their only flowing three-quarter move.
Jonathan Sexton's penalty edged Leinster 11-10 ahead at half-time but Munster took control after the break.
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Leinster reduced the arrears with Fergus McFadden scoring a penalty either side of half time.
It was just a case of trying my hardest for Leinster and seeing what happened.
Felipe Contepomi landed two penalties for Leinster with Ulster's Ian Humphreys and Clinton Schifcofske replying.
Leinster now lead the league table by four points while Connacht are rotted to the bottom.
The Ospreys clinched their crown by beating Leinster 17-12 in last season's Grand Final in Dublin.
Fillol's conversion suddenly left only seven points between the sides with Leinster's talisman hobbling off.
Connacht have been granted a meeting with Leinster, Munster, Ulster and IRFU officials next week.
"We want to apologise to supporters, especially as the Leinster game was also postponed, " added Kelly.
Brian O'Driscoll and Rob Kearney produced superb breaks but poor handling prevented any Leinster tries.
The two-time champions were unable to top the group after Leinster beat Edinburgh 12-3.
Further head injuries followed away against Leinster and at home to Sale in November.
"I thought Anthony Allen, in particular, looks a great prospect, " said O'Driscoll after Leinster's 37-20 win.
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Leinster's Mark McDermott will continue as assistant, with Ulster-based David Haslett remaining as team manager.
Berne touched down for Leinster after just three minutes, with Nacewa converting to make it 7-0.
"It will be very sweet for me playing against Leinster, my home province, " added Murphy.
Leicester go on to face Leinster in the final at Murrayfield on 23 May.
The Blues face Leinster, Opsreys and Ulster in the opening weeks of the Magners League season.
He has overlooked Bath's Butch James, Toulon's Joe van Niekerk and Leinster's CJ van der Linde.
Valentin Courrent's second penalty cut Leinster's lead but Fitzgerald's second try extended the advantage to 17-6.
Yves Donguy's try helped Toulouse claim a crucial bonus point despite Felipe Contepomi's late Leinster drop-goal.
Leinster coach Matt Williams said afterwards that his side had recovered after a "nervous start".
However, injury-time tries from replacement Des Dillon and Gordon D'Arcy brought Leinster's total up to 48.
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