Cardiff beat Munster away last time out in the RaboDirect PRO12, and they responded positively to Madigan's penalty with a flowing back-line move that had the visitors scrambling.
Wales Under-20 starley Rhys Patchell passed to winger Owen Williams who chipped over the head of Darren Hudson, but the excellent David Kearney put Williams under enough pressure and forced a five-metre scrum from which Leinster managed to clear.
After 13 minutes, Patchell brought the Blues level with a 40-metre penalty after Leinster were penalised in their own lineout. Andrew Goodman soon made good inroads for Leinster but when brought down, he was penalised for holding on and Patchell missed the resulting penalty.
The province lost lock Tom Denton to the sin-bin in the 20th minute. An off the ball tackle on his opposite number James Down was seen by referee Peter Fitzgibbon who brandished the yellow card.
It was 14-man Leinster who threatened the scoreboard next though and out-half Madigan restored their lead with a long range penalty which went over off an upright.
Following good pressure from Brendan Macken and Shane Jennings, Blues full-back Jason Tovey knocked on just five metres from his own line which resulted in a Leinster scrum.
The ball squirmed out and Jordi Murphy tackled Harry Robinson into touch. Paterson refused to let the ball go and referee Fitzgibbon awarded Leinster a penalty which Madigan duly converted to put them 9-3 up.
Denton returned from the sin-bin and during his cooling off period, Leinster did not concede a point whilst playing with 14 men.
Three minutes before the interval, Ireland international Isaac Boss scored the visitors' first try of the night to give them further momentum.
Great work by Kearney resulted in decent field position deep in the Blues 22. Three more phases elapsed and scrum half Boss weaved his way through the defence from close range. Madigan made no mistake with the conversion to put Leinster 16-3 in front.
A commanding first half performance from number 8 Murphy was rewarded wih a try on the stroke of half-time. A solid Leinster scrum left Murphy with the perfect platform to pick up and barge his way over the try-line. Madigan added the extras for a 23-3 lead.
Eleven minutes into the second half, the Blues pulled a try back through Tovey. Wexford man Robin Copeland, who was a constant threat, offloaded to the full-back who touched down in the corner. Patchell missed the conversion.
The young number 10 managed to reduce the gap with another three-pointer after 59 minutes. The same player thought he had scored a try but referee Fitzgibbon had already given a knock on against the Blues. Leinster cleared the danger from the resulting scrum.
The Leinster scrum was solid throughout and another powerful set piece from Schmidt's side resulted in a penalty being awarded to them. Madigan kept up his 100% place-kicking record with another good strike to make it 26-11.
Madigan tried to take his personal tally to 19 points but missed with a late drop goal attempt. Shortly afterwards, the influential out-half's cross-field kick almost found the returning Eoin O'Malley who was thwarted by an awkward bounce close to the try-line.
With the last play of the game, the Blues almost narrowed the margin of victory but they could not utilise an overlap and Noel Reid got hold of the ball as Leinster sealed an encouraging win on the road.
Speaking after the game, head coach Schmidt said: "I am delighted with the win, we had 15 guys in camp with Ireland. We had to draw on some of the young guys in some sticky conditions underfoot.
"Jack McGrath did well and so did Jack O'Connell when he came on. Michael Bent was very strong in scrum. Dominic Ryan hasn't had a massive amount of rugby but played very well.
"Madigan kicked very well, Ian was 100% which allows you to build scoreboard pressure. It was good game management from Ian tonight.
"And there is certainly a bit of life left in the old dog, Leo Cullen. He is a workhorse. He got through work that people didn't see. He is a great guy to have for this part of the season."
|Cardiff Blues Score Card|
|Leinster Rugby Score Card|