At 4-4 in the deciding set, Berdych trailed 15-40 and saved two break points.
Although Berdych won the Shenzhen Open in China last month, the Czech player’s form dropped sharply with first-round exits at the Japan Open and the Erste Bank Open in Vienna. In between, there was a second-round loss at the Shanghai Masters.
Losing so many ranking points forced Berdych out of the top 10 for the first time since reaching the 2010 Wimbledon final. It also leaves him needing to reach the semifinals in Paris to have a chance of qualifying for the season-ending ATP finals in London – a difficult task considering he could face Andy Murray in the quarterfinals.
Berdych, the 2005 champion, had 14 aces against Sousa. He will next face either 10th-seeded Roberto Bautista Agut or Gilles Simon.
Seven players vying for the two remaining spots in London.
Dominic Thiem and Marin Cilic, who won the Swiss Indoors on Sunday, held the last two places before this week. David Goffin, Jo-Wilfried Tsonga, Lucas Pouille and Bautista Agut are the other contenders playing in Paris.
John Isner had 14 aces as he reached the second round by beating Mischa Zverev 7-6 (8), 6-4. Isner saved the only break point he faced in the first set and broke Zverev’s serve early in the second.
Isner will next play 15th-seeded David Ferrer, who has beaten the big-serving American seven times in eight meetings. Isner’s only win, however, was in the quarterfinals in Paris five years ago.
Also in the first round, French veteran Nicolas Mahut beat Martin Klizan 4-6, 6-4, 6-3, while Viktor Troicki saved two match points before defeating Adrian Mannarino 6-4, 3-6, 7-6 (5).
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