Portugal captain Ronaldo scored twice from the penalty spot in the second half and added a header nine minutes from time to take his tally in Europe's elite club competition to 80 goals, three more than Barcelona forward Messi.
A howler from Shakhtar keeper Andriy Pyatov let in Karim Benzema for the opener on the half-hour before the visitors were reduced to 10 men five minutes after the break when Taras Stepanenko hacked down Sergio Ramos and was shown a second yellow card.
Real doubled their lead after Ronaldo’s shot hit Shakhtar captain Darijo Srna on the back in the 54th and the referee inexplicably gave a penalty and the Portuguese netted another spot kick nine minutes later after Marcio Azevedo handled.
Ronaldo, who put five past Espanyol in La Liga on Saturday, completed his hat-trick at the Bernabeu when he followed up a saved Marcelo effort to set a Spanish record of 33 trebles, one more than Messi.
The victory gave new Real coach Rafa Benitez a winning debut for the capital club in the competition but came at a cost as their Wales winger Gareth Bale limped off midway through the first half with a calf problem.
Centre backs Raphael Varane and Sergio Ramos were also substituted with knocks and Benitez said the trio would have tests to determine the seriousness of the injuries.
NOT BRILLIANT
"Without playing a brilliant match we still created a lot of chances," Benitez told a news conference.
"I am very pleased to have taken those we did and not to have conceded a goal again," he added.
Real, the record 10-times European Cup winners and 2014 champions, several times went close in the early stages with Bale almost scoring with a clever flick through his legs from Dani Carvajal’s cross in the 13th minute.
Shakhtar were holding their own reasonably well without troubling Real keeper Keylor Navas until Pyatov came out to gather and fumbled the ball straight to Benzema.
The France striker, who missed two other easy chances, cracked the ball into the empty net for his 43rd Champions League goal.
Shakhtar's best chance came in added time when Navas tipped a deflected Alex Teixeira shot over the bar.
(Editing by Toby Davis and Ken Ferris)
