Cristiano Ronaldo equalled the record for most goals in the tournament in one season with his 14th and Gareth Bale and Isco also scored in the quarter-final first leg as Real steamrollered the team who beat them 4-1 in Dortmund in the first leg of last term's semi-final before going through 4-3 on aggregate.
Chasing the record-extending 10th continental crown which has eluded them since their last triumph in 2002, Real dominated an injury-hit Dortmund side who were also missing suspended striker Robert Lewandowski.
The Poland international, who scored all four goals against Real in last year's semi-final first leg, should be back for the return on Tuesday but Juergen Klopp's side must pull off something close to mission impossible to turn the tie around.
"I am very pleased with the match and the result," Real coach Carlo Ancelotti told a news conference before warning that Dortmund, who squandered several chances in the second period, remained a threat.
"We used up a lot of energy in the first half to keep up the intensity and then we held back in the second and tried to counter attack," added the Italian.
"What Borussia showed in the second half is that they are a team with quality who have what it takes to turn the tie around and we have to be careful next week."
Wales winger Bale poked the ball into the net in the third minute at the Bernabeu to put Real ahead and Spain playmaker Isco curled in a second in the 27th.
Ronaldo notched his 14th goal in eight Champions League games this season 12 minutes after halftime, matching a record for Europe's elite club competition jointly held by Barcelona's Lionel Messi and former AC Milan forward Jose Altafini.
It was the Portugal forward's 100th Champions League appearance and the goal, when he picked up a Luka Modric pass and clipped the ball into the net from close range, took his overall tally to 64.
"It's a magnificent result, we are pleased with the 3-0, above all for not conceding a goal," Isco said in an interview with Spanish television broadcaster Canal Plus.
"It's a big step towards a place in the semi-finals," he added.
"The whole defence should get 10 out of 10, and the team as well, the result was more than deserved."
With several thousand yellow-and-black-clad travelling supporters in fine voice high up in the stands, Dortmund went on the attack from the kickoff but were rocked when Dani Carvajal found space in the area and slipped a pass to Bale.
The former Spurs player took one touch and then did well to stretch out a leg and poke the ball past onrushing Dortmund goalkeeper Roman Weidenfeller into an empty net.
Buoyed by the goal, the home side started to dominate and Weidenfeller pulled off an acrobatic save to keep out a Ronaldo free kick in the 12th minute before Isco struck.
Xabi Alonso intercepted the ball near the Dortmund penalty area and when it fell to Isco he sent a low curling effort just inside the post.
Weidenfeller was tested again when Bale arrowed a free kick towards the top corner and Dortmund's woes mounted when captain Sebastian Kehl picked up a yellow card and a suspension for the return leg.
The rain began pouring down at halftime and Dortmund started the second half brightly, almost scoring after a swift break in the 55th.
However, another sloppy pass out of defence led to Real's third and when Modric fed Ronaldo and he showed fancy footwork before beating a stranded Weidenfeller.
Ronaldo has not always received unconditional adoration from the Real faithful since joining in 2009 but he was given a rousing ovation when he apparently picked up an injury and was substituted 10 minutes from time.
Ronaldo has been having treatment on his left knee but Ancelotti said it was nothing to worry about.
Dortmund were comprehensively outplayed and came closest to a goal just before the hour when centre back Pepe blocked a close-range Henrikh Mkhitaryan effort.
Real are through to the Champions League last eight for a fourth consecutive season and have reached the semi-finals in the last three seasons.
"We conceded the goals, we were not compact enough and left big spaces between the lines, as big as I have ever seen them. The goal came early and that did not help, although you expect Real to score at home," Klopp told ZDF.
"Not being compact enough is risky against one of the best attacking teams in the world."