UEFA Champions League holders Real went two up before Romelu Lukaku scored a tap-in for last season's Europa League winners United to ensure a nervy finish.
Meanwhile, United included summer signings striker Lukaku, holding midfielder Nemanja Matic and centre-back Victor Lindelof:
Real were in front in the 24th minute when Casemiro finished after a fine cross from right-back Dani Carvajal. Brazilian holding midfielder Casemiro appeared to be offside, but the goal was given.
It meant this unlikely goalscorer, usually known for his defensive nous, has now made a habit of finding the net on the big stage for Real, per Squawka Football:
The same source noted how Casemiro's goal kept Los Blancos' incredible scoring run in consecutive matches going:
Real were firmly in control as United struggled to keep the ball and muster much of a threat going forward. The Red Devils' most common ploy to try and break down Real's defence was to launch long balls into the channels for Lukaku to use his strength and pace.
Lukaku's efforts weren't helped by a lack of support, as Jesse Lingard, Henrikh Mkhitaryan and Paul Pogba struggled to get close enough to the Belgium international.
One of the reasons Real bossed possession was the movement and technique of Isco. The former Malaga ace constantly roamed midfield, seamlessly switching positions, always showing for the ball and exchanging quick passes with Toni Kroos and Luka Modric.
As Real dominated, football writer Andy Mitten felt the gulf in class was obvious:
United introduced Marcus Rashford for Lingard at the break, but the change did nothing to alter the one-sided pattern of the match.
Real were quick out of the blocks again and saw Toni Kroos sting the palms of United goalkeeper David De Gea from distance. It wasn't long before Los Merengues doubled their lead, though.
Their second came seven minutes into the second half when Bale released Isco and the latter finished calmly.
The ease of the goal prompted James Ducker of the Daily Telegraph to comment on the difference in quality between both sides:
United should have hit straight back, but Pogba saw his header rebuffed by Keylor Navas before Lukaku skied the rebound well over the bar. The Guardian's Jamie Jackson made it clear United's big-money buy simply has to do better:
A two-goal lead should have been padded, but Bale smashed a shot off the underside of the bar. Karim Benzema then slipped when he seemed to have a simple finish after another fine delivery from Carvajal.
Los Merengues would rue those misses when Lukaku made the most of his next opportunity for a tap-in. The ex-Everton man finished from close range on 62 minutes after Matic's shot cannoned off Navas.
Zidane responded by surprisingly removing Bale and star man Isco for Marco Asensio and Lucas Vazquez.
Predictably, Real lost some impetus without Isco, and United should have been level when Mkhitraryan played Rashford in. However, Navas saved the England international's scuffed, low shot well.
The chance came thanks to fine work from Fellaini, who controlled a long ball well before feeding Mkhitaryan with a smart lay-off. Fellaini's formidable aerial presence had made a big difference since his introduction.
Speaking of an introduction, Real's attacking talisman Cristiano Ronaldo came off the bench, and the former United star received a warm ovation from the Red Devils' supporters.
Ramos and Asensio went close for Los Blancos in stoppage time, but there was no further scoring and the Champions League winners held on for a memorable win.
Aside from a few wobbles in the second half, Real were in control, showing the class and style that made them such a force both domestically and in Europe last season.
United aren't at the same level yet, but they at least showed commendable fighting spirit to continue forcing the issue despite lacking quality for much of the night.