The home side were in a strong position at the end of a rain-hit day as the partnership enabled South Africa to reach a total of 364, while Pakistan were 106 for 4 when bad light stopped play and 31 overs were lost.
Symcox, 37, and the 21-year-old wicketkeeper Boucher - the oldest and youngest members of the side - beat the mark of 190 set by Asif Iqbal and Intikhab Alam for Pakistan against England at the Oval in 1967.
Symcox played a tired pull shot to mid-on after scoring 108 in 226 minutes off 157 balls, with 17 boundaries. Boucher, in his second Test, made 78.
Symcox, who had a previous highest Test score of 81, against Pakistan in Faisalabad earlier this season, leapt high in the air as he completed the single which completed his hundred. He went from 90 to 100 in singles.
"I've always wondered what it felt like to score a Test hundred," Symcox said. "I was at the crease when Hansie [Cronje] and Daryll [Cullinan] scored their first centuries and it seemed like something very, very special. Now I know and all I can say is that it is incredibly tough, mentally more than physically."
Only two other No 10 batsmen have made Test hundreds - Billy Read for England against Australia in 1884 and Reggie Duff for Australia against England in 1901/02.Reuse content