The 2013/14 UEFA Champions League group stage got under way on Tuesday night with the first half of fixtures taking place.
Isco opened the scoring for Real in the 33rd minute before Karim Benzema added a second early in the second half before the Portuguese ace fired home the first of his treble from close range just after the hour-mark.
Ronaldo was then on hand to slot home from inside the six-yard box in the 66th minute after Sergio Ramos' header had been kept out before setting up Benzema for Madrid's fifth in the 81st minute.
Umut Bulut pulled on back for the hapless Gala' three minutes later before Ronaldo completed his hat-trick in injury time with a wonderful goal from an angle after dancing around three defenders.
It was the first European game for United not managed by Sir Alex Ferguson since 1985 but it was the same old result for the Red Devils who had Wayne Rooney to thank with the England striker netting a double to take his club goals tally to 200.
The 27-year old found himself unmarked at the edge of the six-yard box to side-foot home Patrice Evra's cross in the 22nd minute before Leverkusen skipper Simon Rolfes, with the aid of a deflection, curled in a leveller ten minutes into the second half.
Robin van Persie restored United's lead in the 59th minute with a wonderful side volley on his right foot from Antonio Valencia's cross before Rooney notched up his milestone after beating Bernd Leno when Emir Spahic's header fell allowing him to run at the Bayer keeper.
Champions League holders Bayern Munich kicked off their title defence with a 3-0 win over CSKA Moscow at the Allianz Arena thanks to goals from David Alaba (a brilliant dipping free-kick), Mario Mandzukic and Arjen Robben (after a deft chip from Alaba) in Pep Guardiola's first European game in charge of the Bavarians.
Elsewhere, Edin Dzeko, Yaya Toure (a cracking curler from range) and Sergio Aguero scored their goals in the space of ten minutes as Manchester City beat Czech champions Viktoria Plzen 3-0 away whilst Juventus needed Fabio Quagliarella's 54th minute goal to salvage a point at FC Copenhagen after Nicolai Jorgensen opened the scoring 40 minutes earlier.
Alex Teixeira scored a double as Shakhtar Donetsk beat Real Sociedad 2-0 in Spain, Benfica got the better of Anderlecht 2-0 in Portugal and Thiago Motta netted a brace to help Paris Saint-Germain hammer Olympiakos 4-2 in Greece.
2013/14 UEFA Champions League scores
Real Sociedad (SPN): 0 Shakhtar Donetsk (UKR): 2 (Alex Teixeira 65'/87') Estadio Anoeta, San Sebastian, Spain - 27,902