- Real Madrid 2-0 Ajax: As it happened
Madrid took the lead in the 31st minute when the ball ended in the back of the net after Gonzalo Higuain and Ajax defender Vurnon Anita had challenged for a corner, and then the prolific Higuain made it 2-0 in the 73rd minute to complete a deserved win for Mourinho's men.
However, if Madrid want to make a serious impression on this year's Champions League having been knocked out at the last-16 stage for the last six editions then they will probably need to improve a great deal on their finishing.
The big-spending Spanish giants had countless efforts on goal but a mixture of good goalkeeping from Ajax custodian Maarten Stekelenburg, the woodwork and poor finishing saved Martin Jol's Ajax from a heavy defeat in their Group G opener.
Higuain, Angel Di Maria and Cristiano Ronaldo all could, and perhaps should, have been celebrating at least a couple of goals each.
Higuain went close early on when he powered a shot into the side-netting, and in the 17th minute the same player was unfortunate to see his curling effort from the edge of the area rebound back off the top of the far post.
Di Maria, who was brought in to replace Karim Benzema on the left wing as Mourinho made a couple of changes to the side that beat Osasuna at the weekend, then saw back-to-back shots saved by Stekelenburg before Madrid took the lead in the 31st minute.
Xabi Alonso's corner into the six yard box was met by Anita but it appeared as though his header hit Higuain before deflecting into the net.
Higuain did not look as though he knew too much about it but what mattered for the home side was that Madrid, looking to win a record 10th European Cup crown, were up and running.
The home fans had voiced their discontent at a poor first-half showing against Osasuna on Saturday but the Bernabeu faithful could have few complaints about their side's attacking intent early on tonight.
Di Maria should have made it 2-0 in the 33 minute when he blazed over and the same player went close again just before the break.
It was an almost identical story in the second half, with Madrid creating numerous shooting chances and four-time European champions Ajax - missing star striker Luis Suarez through suspension - only threatening sporadically.
Ronaldo was denied by a good save from the overworked Stekelenburg, who then did well to parry Di Maria's 25-yard shot before Higuain, having chested down the rebound, contrived to blaze over from close range.
That left Higuain looking to the heavens and Mourinho - who last season became only the third coach in history to conquer Europe with two clubs after leading Inter Milan to glory at the Bernabeu - shaking his head in disbelief.
Madrid's profligacy in front of goal could have come back to haunt them in the 64th minute when Toby Alderweireld fired a low shot not too far wide of Iker Casillas' left-hand post.
Ronaldo spurned another opening before Madrid finally managed to put some breathing space between themselves and the Dutch outfit when Higuain netted his second in the 73rd minute.
Mesut Ozil might have scored himself but, when his shot came straight back to him off Stekelenburg, the Germany international played the ball across the face of goal where Higuain had a simple tap-in.
Higuain missed the chance to net his hat-trick a minute later when he drilled a shot just wide following good build-up play with Ronaldo, before Ajax raced down the other and gave Madrid a scare when Urby Emanuelson curled a 25-yard shot against the crossbar.
Casillas was beaten by that effort but he recovered well to keep out Mounir El Hamdaoui's follow-up shot and ensure dominant Madrid would have a comfortable final 10 minutes.
Source: DSG
