The 28-year-old doubles specialist needed three hours and 42 minutes and had to save match point before seeing off Australian Anastasia Rodionova 6-4 6-7 (7/4) 7-6 (7/3), setting up a clash with world number 16 Sloane Stephens next.
Mattek-Sands said, according to the WTA's official website: "I don't think I've ever played a match that long. The good thing is I showed myself I can last out there and just grind it out."
Former French Open champion Francesca Schiavone bowed out in another long three-set contest, exiting 3-6 6-4 7-6 (8/6) at the hands of Spaniard Silvia Soler-Espinosa. Like Rodionova, Schiavone also had a match point but could not make it count.
Romanian 11th seed Sorana Cirstea battled past German Tatjana Malek, winning 6-4 7-6 (7/5), while 12th seed Varvara Lepchenko prevailed 6-3 4-6 6-2 in an all-US battle against Christina McHale.
There was frustration for 13th seed Tamira Paszek who retired injured after dropping the opening set of her clash with 18-year-old American Grace Min, the former US Open girls' champion.
A notable winner was Andrea Petkovic, the former world number nine who is competing on a wild card. The injury-plagued German has begun her season late, after suffering a knee injury at the Hopman Cup in December, but won two matches in Miami recently and got her Charleston campaign under way with a 6-3 6-0 win against American 16-year-old Taylor Townsend.
Serena Williams is the defending champion and top seed this week.