Paul, ranked No. 31 in the world, fell behind early to Borg, ranked No. 577. But he took care of business and won 26 of 38 total points in the third set to complete the comeback.
Bulgarian sixth seed Grigor Dimitrov was less fortunate, as Czech opponent Jiri Lehecka upset him 6-4, 1-6, 7-6 (5).
Australian fifth seed Alex de Minaur, Swiss qualifier Antoine Bellier, Finland's Emil Ruusuvuori and Sweden's Mikael Ymer also won their matches.
European Open
Swiss qualifier Dominic Stricker, 20, surprised Dutch seventh seed Botic van de Zandschulp with a 6-2, 6-4 victory in the first round in Antwerp, Belgium.
Stricker saved all four break points he faced and had a 5-2 edge in aces to dispatch van de Zandschulp.
No. 6 seed Francisco Cerundolo of Argentina and No. 8 seed Yoshihito Nishioka of Japan needed three sets to get by their first-round opponents. Cerundolo rallied to beat Marc-Andrea Huesler of Switzerland 5-7, 7-6 (3), 6-3, and Nishioka outlasted French qualifier Luca Van Assche 5-7, 6-2, 7-6 (1).
David Goffin earned a tight victory over wild card Gilles Arnaud Bailly 7-6 (7), 5-7, 6-4 in an all-Belgian battle that lasted 3 hours, 12 minutes. Constant Lestienne of France and Jaume Munar of Spain also advanced.
Tennis Napoli Cup
Two seeded players bowed out on the first day of main-draw action in Naples, Italy.
Portugal's Nuno Borges toppled No. 7 seed Albert Ramos-Vinolas of Spain 7-5, 7-6 (5), and Pedro Cachin of Argentina upset No. 8 seed Adrian Mannarino of France 6-1, 3-6, 6-4.
Fifth seed Miomir Kecmanovic of Serbia was spared from the upset bug. He beat Italian wild card Flavio Cobolli 6-1, 6-2.
Japan's Taro Daniel and Colombia's Daniel Elahi Galan also opened the tournament with wins.
