Cristiano Ronaldo's hat-trick helped Real Madrid to a 4-0 victory over 10-man Shakhtar Donetsk in the Champions League on Tuesday although it came at a cost with injuries to three key players.

Rafael Benitez will likely be judged on Madrid's showing in the competition this term and, in his first European outing at the helm, Ronaldo's treble helped mask knocks to Gareth Bale, Raphael Varane and Sergio Ramos.

Madrid had been frustrated for much of the opening half hour prior to Bale's withdrawal, before Andriy Pyatov spilled a simple cross, allowing Karim Benzema an easy finish.

Benitez replaced Varane with Pepe at the break before Taras Stepanenko's dismissal made Shakhtar's task all the more difficult, the midfielder flying into a second-half challenge on Ramos having already been booked after 32 minutes.

Ramos was then taken off before Ronaldo completed his hat-trick inside 26 second-half minutes - tucking home two penalties to move two goals clear of Lionel Messi in the competition's all-time scoring charts.

And Ronaldo, who put five past Espanyol at the weekend, nodded home a rebound after Marcelo's shot was blocked to wrap up a simple win.

Varane's inclusion was one of two changes made by Benitez and the Frenchman curled an effort over the crossbar following a short corner two minutes in, before heading wide from inside the area soon after.

Ronaldo made his first contribution by playing in Benzema, although the Frenchman missed the target after rounding Pyatov, with Ronaldo cleverly turning and shooting wide from inside the area in Madrid's next attack 15 minutes in.

The visitors were almost handed an opener against the run of play when Keylor Navas failed to control a Varane backpass - the goalkeeper just able to keep the ball out - before Bale's withdrawal added to Madrid frustrations.

The Wales international went down holding his left calf and was quickly replaced by Mateo Kovacic before Benzema made the most of Pyatov's goalkeeping error to open the scoring 30 minutes in.

Benzema was afforded the simplest of finishes after the Shakhtar goalkeeper spilled an Isco cross from the left.

An Olexandr Kucher interception denied Ronaldo a one-on-one opportunity following a quick break within two minutes of the restart before Stepanenko's senseless sending off prior to the hour mark.

With a man advantage, Madrid continued to dominate, doubling their lead from the spot when Ronaldo's goalbound effort was harshly deemed to have struck Darijo Srna's hand.

The Portugal man converted the penalty with ease and found the bottom left corner from the spot again eight minutes later after Marcio Azevedo was deemed to have handled.

And Ronaldo - who became his club's leading La Liga goalscorer at the weekend - wrapped up another hat-trick nine minutes from time.