Cristiano Ronaldo scored after 18 and 70 minutes while Luka Modric (50) and Dani Carvajal (52) also struck to put the 10-times European champions in complete command on a freezing night in western Ukraine.
The temperature then soared quickly, on the field at least, as Shakhtar netted three times in the closing stages.
Brazilian midfielder Alex Teixeira converted a penalty after 77 minutes before Dentinho chested the ball into the net from a corner.
Teixeira was again on target with an elegant drive in the 88th minute as the hosts gave Real a huge fright.
Real have 13 points from five matches, three ahead of Paris St Germain who also qualified by beating Malmo 5-0 in Sweden.
PSG are sure to finish second because they have an inferior head to head record against Real. Shakhtar and Malmo both have three points.
Ronaldo opened the scoring with a header and grabbed his second goal of the night on the rebound after his initial attempt was blocked by a defender.
The Portugal forward also played a part in the other two goals by the visitors before Shakhtar came storming back as Real conceded their first goals in this year's competition.
(Writing by Igor Nitsak; Editing by Tony Jimenez)
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