Real Madrid got their UEFA Champions League campaign off to a flying start with a comfortable 4-0 win over Shakhtar Donetsk at the Santiago Bernabeau behind a hat trick from Cristiano Ronaldo on Tuesday night.

Ronaldo also made history as he became the tournament's all-time scoring leader with 80 goals, taking him three past his archrival Lionel Messi. It was also his third Champions League hat trick, a remarkable feat on its own.

The torrid Ronaldo followed up his five-goal show in La Liga on the weekend with an historic hat trick. Scoring twice from the spot and once off a header from open play, this was another big night for a man widely considered to be the hardest-working but second-greatest player in the game. Driven to remove himself from the shadow of Barcelona's Messi, Ronaldo seems to be making an early season statement with his goal count, and it will be fascinating to see if his rival can keep pace.

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This was expected to be a gripping match but it lived up to its billing for only about a half, as a red card to Taras Stepanenko and a dreadful error by keeper Andriy Pyatov ended the game as a contest. Shakhtar, proud but greatly diminished from last season with the loss of Douglas Costa to Bayern, did put on a decent show before wilting once reduced to 10 men against the Spanish giants.

In fact, Marcio Azevedo had the first real chance of the game, and he should have done better with it. Instead of passing the ball to his runner, he scuffed his shot wide in the sixth minute -- but it was a warning for Keylor Navas and manager Rafa Benitez, and the former Liverpool boss was immediately out of his dugout to organize his side. For a time, Shakhtar proved to be quite good at keeping the ball once they had it, using Fred and Alex Teixeira to pivot the attack, and sending fullbacks Dario Srna and Azevedo rampaging forward on Navas' net. But they lacked cutting edge in front of the net, and soon Real made them pay.

In fact, Karim Benzema almost got Real on the board in the 15th minute, with Luka Modric and Ronaldo linking up well to set up what should have been a sitter. But Benzema, normally so composed on the break, instead skied his shot, drawing groans from the crowd.

The gloom deepened. Gareth Bale pulled up with an apparent calf injury, and had to be removed just after the half hour for Mateo Kovacic. The extent of Bale's injury was not immediately known, but he looked unhappy as he hobbled off.

''We will have to wait a few days to see how these injuries progress,'' Benitez said. ''(Raphael) Varane and (Sergio) Ramos are dealing with knocks, but Gareth already had a problem like this last year. We'll see.''

But immediately after Benzema finished off what was likely one of the easier chances of his career, Isco flighted in an easy cross, and there appeared to be a miscommunication between Yaroslav Rakitskiy and his keeper, which resulted in Pyatov spilling the ball at Benzema's feet. The goal extended a remarkable streak for Benzema, who has scored at least once in 11 straight Champions League campaigns.

Real shifted to a straightforward 4-4-2 system and started to use Ronaldo to pry Shakhtar apart. He had two great chances: the first, a good cross from Marcelo that he did not seem to anticipate coming through the pack, and he was puzzled when it bounced off him and into touch; then, he missed just wide prior to the halftime whistle.

However, Ronaldo finally got his goal. Srna was judged to have blocked his shot in the 54th minute with his hand by the goal-line judge, and referee Ivan Bebek pointed to the spot. It was a horrible decision -- replays showed the shot clearly came off Srna's back, not his hand -- but Ronaldo stepped up and sunk his 78th goal to put the game to bed.

By that point, things had gone from bad to worse. Stepanenko correctly saw his second yellow and then a red after a hard foul on Ramos that gave Bebek no choice. Bebek would point to the spot again in the 62nd minute when Azevedo blatantly handled a ball from Dani Carvajal. There was no doubt about that call, and no doubt about the result, either, as Ronaldo buried that spot kick as well to take his total to 79.

After that, the game was done. Ronaldo had free reign to run at Pyatov's net and at a man down, Shakhtar had no answers. He would snatch his third goal to complete the hat trick when Pyatov could only parry Marcelo's shot into Ronaldo's path.

Shakhtar will not get a respite either, as they next face a tough Paris Saint-Germain side that easily brushed aside minnows Malmo on Sept. 30. Real Madrid, on the other hand, have an easy jaunt to Sweden and will be feeling pretty comfortable about their chances.

''We didn't play brilliantly but we still created many chances,'' Benitez said after the win. ''It was a difficult match to play. They have a lot of speed, many quality players and know how to take advantage of counter-attacks.''

Information from The Associated Press contributed to this report.