Wawrinka, playing in his first Tour Finals, defeated Tomas Berdych 6-3, 6-7 (0-7), 6-3 for the early Group A lead and del Potro got the first point in Group B with a 6-7 (4-7), 6-3, 7-5 win over Richard Gasquet, who is ranked No. 9 and was the last player to qualify for the tournament.
Del Potro, fifth in the world rankings, dropped his served just twice on the day. The second came as he was serving for the match at 5-4 and Gasquet kept alive with a break at love. Del Potro answered with his fourth break of the match and then held serve at 15 for the win.
Both players had a first-set break before Gasquet took the lead by winning four of the last five points in the tiebreaker. Del Potro didn't face a break point in the second set and posted a fourth-game break that allowed him to even the match.
Wawrinka, No. 8 in the world rankings, defeated the sixth-ranked Berdych with a very solid effort in the first match of the tournament. The only blip on Wawrinka's performance was the shutout during the tiebreaker.
Wawrinka, who qualified for his first Tour Finals last week, posted the only break of the first set and the second set played even until the tiebreaker when Berdych tied the match.
Berdych won 81 percent of the points when he got his first serve in but Wawrinka won 26-of-58 of the points off Berdych's second serve. That was especially apparent it the third set when Wawrinka took 11-of-15 points in that situation. Four of the points Wawrinka won in his fourth-game break came on second serves.
Tuesday's schedule is the same as last Saturday's Paris Masters semifinals. World No. 1 Rafael Nadal takes on defensive champion David Ferrer in Group A and second-ranked Novak Djokovic, who is the defending champion, faces No. 7 Roger Federer in Group B. Djokovic beat Federer in last year's World Tour Finals title match.
Notable deaths of 2014 [PHOTOS]