No.2 seed Badosa had no answer to the brilliance of Halep in her homeland as the relentless Romanian won 6-3 6-1 at the Caja Magica.
Unseeded two-time grand slam champion Halep took just one hour and 17 minutes to eliminate Badosa, breaking three times in the first set and twice in the second.
Halep, in a new era with Patrick Mouratoglou in her corner, won 84 per cent of points when she landed her first serve in, staying in the hunt to win this tournament for a third time with the French Open on the horizon.
The former world No.1 will face Coco Gauff for a place in the quarter-finals after the American's 6-1 2-6 6-4 late-night defeat of Yulia Putintseva.
Gauff, the No.14 seed, racked up 10 double faults and was pushed all the way by Putintseva, but served out the match after securing a third break in a tight final set.
Ons Jabeur earlier advanced into the third round at the expense of Varvara Gracheva, recovering from a second-set bagel to win 7-5 0-6 6-4.
Jabeur faces a meeting with Belinda Bencic after the Swiss dispatched Karolina Muchova 6-3 4-6 7-5.
Victoria Azarenka came from a set down to beat Tamara Zidansek 3-6 6-1 6-3 to set up a meeting with Amanda Anisimova, who also had to come from behind to dispatch Petra Martic 3-6 6-3 6-2.
Ekaterina Alexandrova and Marie Bouzkova also progressed in the Spanish capital.
