Del Potro was projected to switch spots with Anderson in the world ranking, with del Potro going from ninth to eighth. The 29-year-old Argentine star beat three straight players ranked ahead of him in the hard-court event, topping No. 6 Dominic Thiem in the quarterfinals and No. 5 Alexander Zverev in the semifinals.
"It's a very special tournament to me,'' said del Potro, the 2009 U.S. Open champion. "I beat three top-10 guys in the same tournament, which is very important for myself. I'm so glad to win my 21st title playing in Acapulco.''
The 6-foot-6 del Potro won for the first time since successfully defending his Stockholm title last year.
"He's a very dangerous guy,'' del Potro said about Anderson. "His serves are so strong, but I got lucky in the important moments of my return games. I broke just twice and that was the key of the match.''
Anderson tweaked his left leg on del Potro's lob and received treatment at 1-1 in the second.
"It was a little bit uncomfortable at first,'' Anderson said. "I think in the bigger picture of things it didn't really affect things too much,'' Anderson said. "I think Juan Martin played really well. He's obviously a tough competitor and a great player. I just needed to do a little bit more today.''
He won the New York Open two weeks ago for his fourth career title.
"I can take a lot of confidence going into Indian Wells and Miami, two tournaments I really enjoy playing. I feel like I'm playing really good tennis,'' Anderson said. "As always, I'll pick myself up. I'll try to learn as much as I can from tonight's match.''
The 28-year-old Tsurenko, from Ukraine, won her fourth WTA Tour title and first since her victory last year at Princess Mundo Imperial.
"It's such a special tournament for me,'' Tsurenko said. "It was amazing.''
Seeded seventh, she was three points from losing the match in the second set in the match that took 2 hours, 45 minutes.
"Stefanie, it was an unbelievable match,'' Tsurenko said. "It was almost three hours. We both were nervy and we were still fighting to the end. Thanks for this match and for this experience.''
Germany's Tatjana Maria and Britain's Heather Watson won the women's doubles in their first tournament together, topping Americans Kaitlyn Christian and Sabrina Santamaria 7-5, 2-6, 10-2.