Real Madrid's Gonzalo Higuain celebrates after scoring the second goal against Ajax during their Champions League Group G match at the Santiago Bernabeu stadium in Madrid on Wednesday. Real easily won 2-0 to give Jose Mourinho a winning bow in this season's Champions League as coach in Madrid. [Andrea Comas / Reuters]

Real Madrid's bid to win a 10th European Cup began with a 2-0 win over Ajax at the Santiago Bernabeu in its Group G opener on Wednesday.

Coach Jose Mourinho won the Champions League with Inter Milan at the Bernabeu in May and his European bow with Real was a success, with an own-goal and a Gonzalo Higuain strike sealing a comfortable victory.

An own-goal from 21-year-old defender Vurnon Anita gave Mourinho his first European goal as Real coach on 31 minutes and Higuain scored on 73 minutes with his first strike of the campaign.

It was three points and another clean sheet for Real, which has yet to concede a goal in its three games under Mourinho, who believes Real is ready to win the trophy for the first time since 2002 despite failing to get past the last 16 stage for the past six seasons.

Madrid should have won by more and Mourinho said it was just a matter of time before someone will be routed by his Real side.

"We played very well, pressured well and didn't let them play how they like to," said Mourinho. "One day some poor team is going to pay for all these chances that we are missing."

Madrid fans jeered their team in Saturday's 1-0 league win over Osasuna and Cristiano Ronaldo, the world's most expensive player, had caused a stir by saying the supporters should spend their energy supporting their team rather than whistling.

Mourinho refused to discipline Ronaldo over the outburst and the Portuguese star started on the right wing with Argentine Angel di Maria on the other flank to supply target man Higuain.

German internationals Sami Khedira and Mesut Ozil made their Champions League debuts for Real, as did Mourinho, who is trying to become the first man to win the Champions League with three different clubs, having won one crown with FC Porto in 2004 and last year's trophy with Inter.

Ajax coach Martin Jol had to do without Uruguayan international striker Luis Suarez through suspension but still went for the jugular by starting with two strikers.

The first openings all fell to Higuain, who hit the side-netting with a fierce shot and then on 17 minutes the Argentine beat two players and cracked a shot against the crossbar with goalkeeper Maarten Stekelenburg well-beaten.

It was a warning four-time winner Ajax did not heed, and on 31 minutes Real made the breakthrough.

Ajax failed to clear a Xabi Alonso corner from the left and defender Anita got himself in trouble heading the ball into his own net, although Higuain tried to claim the goal.

It was more of Madrid in the second half as Higuain went on a great solo run, showing a turn of pace to bear down on goal, but his shot was blocked.

Ronaldo then saw a left-footed drive saved by the busy Stekelenburg and Higuain missed another golden opportunity by volleying over from close range, prompting Mourinho to throw his hands up in despair at another glaring miss.

Higuain made amends, taking advantage of great work from Ozil and di Maria to slot home from close range on 73 minutes to wrap up the game.

Real goalkeeper Iker Casillas had been a bystander the entire match, but Urby Emanuelson rattled his crossbar with a looping shot as Ajax finally created a chance.

"We lost against a team that knows how to defend and keeps possession," said Jol. "We lost because we have less experience than Real Madrid.

"We played with 13 players from the youth system tonight. Money is very important in football and it is difficult for Ajax to be back among the big teams."

Real had to settle for a 2-0 scoreline that did not reflect its dominance, and the nine-time European champion travels to Auxerre on Sept 28 for its next group match.