PSG opened the scoring at the Parc des Princes after four minutes when John Terry's headed clearance fell to Ezequiel Lavezzi and the Argentine forward thumped a half-volley past Petr Cech.
Eden Hazard grabbed a crucial away goal for Chelsea F.C. from the penalty spot after 27 minutes after Brazilian defender Thiago Silva fouled compatriot Oscar.
PSG restored their advantage on 61 minutes, however, thanks to a David Luiz own goal before Javier Pastore waltzed into the area and fired a shot past Cech at his near post in stoppage time.
Real flew out of the traps against Dortmund F.C. and took the lead on three minutes when Gareth Bale collected Daniel Carvajal's pass and poked the ball under goalkeeper Roman Weidenfeller.
Carlo Ancelotti's side continued to swarm all over last season's beaten finalists and Isco's precise strike from the edge of the box doubled Real's advantage on 27 minutes.
The fleet-footed Cristiano Ronaldo added a third on 57 minutes as he skipped round Weidenfeller to give Real a comfortable cushion and equal Lionel Messi's record of 14 goals in the competition in one season.
In Tuesday's quarter-final first legs, holders FC Bayern Munich were held to a 1-1 draw at Manchester United F.C. and FC Barcelona drew 1-1 at home to Spanish rivals Atletico Madrid. The second legs will be played on April 8 and 9.