In the absence of the injured Jonathan Sexton, Madigan has been a revelation for Joe Schmidt's side this season, kicking goals in metronomic fashion as Leinster remain unbeaten in the RaboDirect PRO12 in 2013.
But it was not just from the kicking tee that Madigan impressed against Glasgow, the effervescent stand-off carrying with real intent and breaking the gain-line seemingly at will.
Gregor Townsend's men arrived at the RDS in fine form having dropped just one possible league point over the past six rounds and it was the Scottish side that started the stronger.
After a cagey start an attacking lineout in the 11th minute gave Glasgow the perfect platform and Ed Kalman went over for his first-ever try in the RaboDirect PRO12 after superb work from Josh Strauss, slipping his tackler and offloading to the prop as Duncan Weir added the extras.
Two minutes later Madigan punished Scottish indiscipline and reduced his side's arrears but Weir had soon added a penalty of his own to make it 10-3 with 20 minutes gone.
The game then began to really open up as the Warriors' off-loading game, with the odd handling error thrown in, created an end-to-end encounter in stark contrast to Leinster's cagey 6-0 win in the reverse fixture back in November.
Another Madigan penalty in the 24th minute meant the Warriors were only 10-6 to the good but it was the visitors who struck next and in fine style.
DTH Van der Merwe wriggled his way free down the left flank, incredibly not stepping into touch before his inside ball found the supporting Peter Horne who went over for the try.
Weir's conversion made it 17-6 in the 34th minute and the challenge was there for Townsend's side to see if they could maintain that lead until half-time.
But within moments Leinster had reduced the deficit as Madigan again was on target from the kicking tee after the Warriors went off their feet in defence at the breakdown.
The Irish province were very much on the front foot as the half drew to a close, Andrew Conway and Madigan both making clean breaks that took them deep into Scottish territory.
But they could not open their try account before the interval, instead settling for a fourth Madigan penalty of the half that kept his side in touch at 17-12, Weir missing a drop goal for Glasgow as time expired.
After the interval it was Glasgow who had the first good chance, Madigan knocking on deep in his 22 to set up a great platform for the Warriors.
Winger Tommy Seymour nearly broke through but after the ball was recycled Nikola Matawalu's inside ball caught Moray Low unawares and the knock on allowed Leinster to clear their lines.
The game was being played in the same breathless fashion as the first, handling errors breaking up momentum but referee Nigel Owens happy to play long advantages as both sides looked to attack from every part of the field.
It was Glasgow who were still just shading proceedings and they signalled their intentions just before the hour mark by turning down a kickable penalty in favour of a kick to the corner.
But once again they failed to make their advantage count as Leinster replacement Jamie Hagan won a crucial turnover and again allowed Madigan to relieve the pressure with a clearing kick.
Both sides were being wasteful in good field position and it was Leinster's turn on 65 minutes to knock on in sight of the try line after yet another searing break from Madigan.
For all the chances in the second period the game entered the final ten minutes with no points on the board since the first half so the next score was always going to be key.
And it was Leinster, cheered on by an inspired RDS crowd, that drove forward after Madigan again used his pace to break clear from halfway.
And when the ball was recycled to the right a couple of phases later it was inevitably the fly-half who scampered over from close range after a smart sidestep.
And the youngster added the extras to put Leinster in front for the first time in the match at 19-17.
A 77th minute Madigan penalty increased the lead out to five points but still Glasgow came back and had the chance to win it but for some frantic try-line defending from Leinster as the clock ticked round to 80 minutes.
And when a long Horne pass out to Seymour was ruled forward the chance was gone and Madigan and co had grabbed a crucial hard-fought win.
|Leinster Rugby Score Card|
|Glasgow Warriors Score Card|