The Bernabeu side had by far the better of the first half as they created the better opportunities, pressed high up the pitch and scored twice in quick succession through Gonzalo Higuain and Angel Di Maria.
After halftime, it was a reversal of roles between the sides, with Real unable to provide their previous link-up play between midfield and attack, and Zaragoza looking the more adventurous and aggressive side.
It took another pair of quick goals, scored in the final minutes of the game, to seal the victory for Real Madrid. Michael Essien and Luka Modric scored them, to rob the away side of any lingering hopes they might have had.
Here are six things we learned from the game in Madrid.
Gonzalo Higuain was again chosen to start centre-forward for Real Madrid ahead of Karim Benzema and proved the wisdom of his selection with another goal to open the scoring.
The goal was a true poacher's finish, swept home from close range after a decent save from Roberto from Raul Albiol's initial header.
Higuain now has seven goals in seven league starts this season, showing just why Mourinho is intent on keeping him in the side.
He maybe doesn't offer as much in the build-up play as Benzema or maybe only figures in the game in bursts, but Higuain is a great finisher when in form.
As Real Madrid dropped off the pace in the second half, he was replaced by the French striker, but Higuain had done his job by then.
At 2-0 up going into half time, Real Madrid were cruising. Zaragoza had offered very little threat to Iker Casillas' goal and Madrid would have been confident of adding to their tally after the break.
However, it didn't work out that way for most of the second half—Madrid sat back, their passing got sloppy and Zaragoza's confidence increased. The away side hit the crossbar and then, with the scoreline still at 2-0, scored a perfectly good goal through Helder Postiga.
It should have been the Portuguese striker's fifth goal of the season—but he was flagged offside.
Postiga wasn't offside.
He wasn't even close. It was a fine goal, well worked and very well finished, but regardless, it didn't stand.
Real Madrid benefited from it as they went on to remain under pressure before wrapping up the win later on.
In the other "top of the table" game, Barcelona similarly got off with a shocking offside decision, this time as Jordi Alba was bizarrely allowed to run on with the ball and score Los Cules' third goal, despite being a good three yards offside.
The poor decisions from the officials just keep on coming. Today they didn't affect one more than the other out of Real and Barça, but that won't always be the case.
As much as Real Madrid dominated the first half against Real Zaragoza, they were poor and sloppy in the second half.
Manager Jose Mourinho grew visibly more agitated as the match wore on and eventually made his three substitutions within the space of 13 minutes as he sought to halt the flow of the game towards his team's goalmouth.
Benzema and Jose Callejon were the attacking changes, in place of the first half goalscorers Higuain and Di Maria. Nacho also came on in defence for his first La Liga appearance of the season.
None of the subs were designed to alter Real's formation, but were instead counted on to hold the ball up better and get involved more—in the case of Callejon, in counterattacks and working back to win the ball.
Real ran out comfortable winners in the end, which is the main thing, but Mourinho will have reason to be very disappointed and somewhat concerned with the performance given to him by his players after the break.
Two goals in two minutes from Real Madrid gave them an ultimately unassailable lead, but there was little more that Zaragoza goalkeeper Roberto could have done to keep the ball out of his net.
For the opener, he made a fine point-blank save low to his right to keep out a firm downward header from Albiol, and no defender was quick enough to react before Higuain fired home from barely three yards out.
Again for the second goal, Roberto made an initial save from Di Maria, which the winger was quickest to, and with no defender even able to close him down, he curled the ball beyond the prone stopper for 2-0.
Late in the game, Roberto was again exposed by a defence unable to cope with Madrid on the break for Essien's goal. And finally, after yet another excellent save from Ronaldo, Modric scored the final goal which was deflected past Roberto after his defenders were unable to clear their lines properly.
Four goals put past him, yet Roberto can be justifiably encouraged with his own performance.
Xabi Alonso and Sami Khedira have been the established central midfield pairing for Real Madrid for some time, but against Real Zaragoza that job fell to new signings Michael Essien and Luka Modric.
With the on-loan Chelsea midfielder doing the holding role, winning the ball back and recycling possession in deeper areas in the first half, Modric was allowed to roam the width of the penalty area in the attacking third and help structure chances down both flanks.
The two had no trouble before halftime and looked to be a competent and complementary pairing for each other. But then, after the break, they were completely overrun in the middle and remained unable to control the game for their team.
Out of all the Real Madrid players who completed the 90 minutes, Essien (88 percent) and Modric (85 percent) had the two highest pass completion rates.
Essien also made four interceptions, two tackles and to top it all off, scored the killer third goal late in the game—before Modric added his own name to the scoresheet.
They might not remain the first choice pairing in the middle for Mourinho, but they at least showed that they can play together well and offer the manager another option whenever required.
Being wasteful might seem a strange accusation to level at the Spanish top flight's second-highest scorer, but Cristiano Ronaldo takes a phenomenal amount of shots every match.
He has by far the highest average number of shots per game in the entire league (seven per match) but has just a 15 percent shot conversion rate.
Compare that with the other highest scorers in the division: Leo Messi at 23 percent, Falcao with 32 percent and Gonzalo Higuain at 28 percent.
Against Zaragoza in particular, Ronaldo took a massive nine shots and failed to score—though he did hit the crossbar with an incredible free kick from 35 yards.
He'll no doubt end up being one of the top two scorers in the league yet again, and so far he has a better record than a goal every game this season, but he does take a massive, huge amount of shots to get there.
Statistics from whoscored.com.