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Anderson was in trouble early losing the first set tiebreaker but finally reigned in his Dutch counterpart after four sets.
The big serving South African was ruthless in the fourth set and ensured that the teams head into the doubles level on Saturday.
Anderson, who gifted Schoorel the first set with a double-fault on set point, came back in the second as he broke in the ninth game to take the set 6-4.
The third set went according to serve with Anderson improving his service. He served to love in the eighth game to make it four games all.
Schoorel had a set point at 5-4 up on Anderson's serve but failed to capitalise with his return sailing long.
Anderson put together a strong service game trailing 5-6 to send the set into a tiebreak. His stronger serve paid dividends in the breaker which he won 7-4 to take a two sets to one lead.
Anderson carried his momentum into the fourth set as he broke Schoorel's serve in the second game and was quickly off to a 3-0 lead.
The South African, ranked 35 in the ATP rankings, sealed the result in the next game when, on break point, he struck a backhand winner down the line to take his lead to 4-0.
Anderson won his next service game to win the set 6-1 and level the tie heading into the weekend.
Earlier Rik de Voest lost to Robin Haase of the Netherlands 7-6 (7-5), 3-6, 0-6, 4-6.
Haase managed his temper after disagreements with line judges and the chair umpire to overcome the South African.
The doubles match will be played on Saturday, starting at noon, with Wesley Moodie and Izak van der Merwe against the Dutch pair of Jesse Huta Galung and Igor Sijsling.
The pairings can be changed up to one hour before the start of the match and both captains may be tempted to change the lineup.
Sunday will see the reverse singles with Anderson playing Haase and De Voest taking on Schoorel.
