The 23-year-old tied the score in the 69th minute, running onto a pass into the penalty area and chipping goalkeeper Jeroen Zoet with a left-footed shot from about 12 yards. Altidore has 17 league goals to go along with seven in the Dutch Cup.
Dempsey scored 23 goals for Fulham last season, including 17 in the English Premier League, three in the FA Cup and three in the Europa League. He transferred to Tottenham in August.
Mart Lieder scored his second of the game for host Waalwijk in the 76th.