It took Pospisil nearly two hours to earn his first win at the Miami event.
Pospisil claimed a key break with del Potro serving for the second set at 5-4. He again escaped trouble by saving two set points in the tie-break before closing out the match.
The 24-year-old Pospisil will meet No. 9 seed Grigor Dimitrov in the second round.
Del Potro, ranked No. 616 in the ATP Rankings, played just four tournaments in 2014 before undergoing surgery on his left wrist last March.
"I don't feel frustrated," del Potro said. "I have to take the positive things on my comeback. The score doesn't matter for now."
Del Potro had been sidelined with a lingering left wrist injury. The 2009 U.S. Open champion had wrist surgery a year ago and played in just four tournaments in 2014, and his ranking has fallen to No. 616.
Rustiness showed in the second set, to the disappointment of a partisan stadium crowd rooting for the Argentine. He served at 5-4 and was broken. He double-faulted holding a set point, lost another set point and double-faulted again on the next-to-last point.
Del Potro converted only one of six break-point chances and hit just nine winners to 36 for the 60th-ranked Pospisil.
"I didn't serve well in the special moments," del Potro said. "But now I'm OK. Just playing the tournament and being here means a lot for me."
Del Potro said he felt fine physically after the match. He said his wrist is not yet 100 per cent, but it's improving week by week.
"It doesn't matter how long it takes me to be at the top again," he said. "I just wanted to play tennis and without pain."
Former No. 1 Caroline Wozniacki won her opening match against American Madison Brengle, 6-0, 6-1. Wozniacki is seeded fourth, and all seeded players had first-round byes.
No. 7-seeded Agnieszka Radwanska, the 2012 champion, beat Anna Schmiedlova, 6-4, 7-5. No. 9 Andrea Petkovic topped American Christina McHale 6-2, 6-2.
No. 2 Maria Sharapova and No. 16 Venus Williams were scheduled to play their opening matches later Thursday.
In other men's play, American Steve Johnson lost to Mikhail Kukushkin, 6-4, 3-6, 6-2. Former Australian Open runnerup Marcos Baghdatis was eliminated by Simone Bolelli, 6-2, 6-2.
Martin Klizan won and will face No. 1 Novak Djokovic in the second round Saturday night.