Real Madrid, whose indifferent domestic league form has left them currently eighth in the Spanish first division, capitalised on an opening own goal by Vasco to regain the form and pride that carried them to the European Cup last May.
"This win will give us impetus for the rest of the season," said the Real Madrid coach, Guus Hiddink. "Tonight we were a bit lucky with the first goal, but we kept attacking and that's what won it for us."
Real, skilfully marshalled by Fernando Hierro and Manuel Sanchis at the back and inspired by Raul in attack, gave a battling display that was ultimately too good for the Brazilian side, who mixed some excellent approach play with periods of sluggish mediocrity, possibly due to spending 12 days in Japan without a match.
"We just gave Real too much space to do what they wanted. They took the few chances they had, we didn't," the Vasco coach, Antonio Lopes, said. Vasco had 15 shots on goal, one more than Real.
In a spirited game in which six yellow cards - three to each side - were handed out, Vasco played their part in an open, attacking match which tipped Real's way after 25 minutes when Naza headed into his own net when it looked easier to clear. The goal came after the Dutch international Clarence Seedorf found Roberto Carlos with a long-range crossfield pass. The Brazilian collected the ball wide on the left and whipped in a speculative cross to where Naza, standing alone six metres from his own goal, appeared to lose his sense of direction and headed the ball past Carlos Germano and into his own net.
The Brazilians changed their tactics in the second half opting for longer balls that put the Real defence under increasing pressure and in the 57th minute they were rewarded. The Real goalkeeper Bodo Illgner parried two shots at close range and Real appeared to have weathered the danger with a high lofted clearance to the edge of their own box. However, Juninho, whose namesake plays for Real's city rivals Atletico, did superbly, trapping the ball with his left foot, cutting inside a defender and unleashing an unstoppable rising shot with his right foot from 20 yards.
Both teams went close to scoring and Real could have taken the lead after 78 minutes but Savio's powerful downward header was saved by Carlos Germano.
From the break Felipe went on a penetrating run deep into the heart of Real's territory, leaving two defenders in his wake, but his angled shot, with only Illgner to beat, bounced agonisingly wide of the far post.
Raul, though, made no mistake at the other end with just seven minutes to play. Another long, raking pass from Seedorf found Raul, who brilliantly eluded two defenders before planting a perfectly-placed curling right- foot shot wide of the goalkeeper for the winner.
That goal, and his overall contribution, earned him a Toyota car as man of the match from the sponsors.
Real, whose only previous victory in this competition came in the inaugural match in 1960, followed Ajax (1995), Juventus (1996) and Borussia Dortmund (1997) as recent European winners - the first time that teams from Europe have triumphed for four successive seasons in the competition.