Nadal, who returned to the courts with the Brisbane International about a year after his injury, faced Australian Thompson in the quarter-finals.
Thompson, who defeated Nadal, who has 22 grand slam championships in his career, 2-1 in sets of 5-7, 7-6 and 6-3, became the side that advanced to the tour.
Thompson will face Bulgarian tennis player Grigor Dimitrov in the semi-finals.