The 39-year-old Serbian was struggling physically but pushed through the second-set decider for his first win at any event since Wimbledon in July.
"It's a great pleasure to be back in my happy place," Djokovic said after the match, adding that the conditions and atmosphere in Beijing suit his game.
"Obviously I'm a completely different person and player than I was 11 years ago when I played here last but thankfully I kept the streak going and hopefully I can do it again," he said.
The former world number one is set to meet wildcard Bu Yunchaokete of China in the second round.
Fans packed the stands in Beijing to watch Djokovic, a firm favourite in China who has never lost in Beijing in 30 matches - although this was his first match at the event since 2015.
He delighted the crowd with an ace to end the first game and saved two break points after a pair of double-faults to win the first set.
Djokovic has had health issues in recent months and struggled to pick up points at the start of the second set, using his racquet to stretch his back between games and needing a medical timeout as a trainer worked on his right shoulder.
But he forced a path to victory in one hour and 50 minutes, clinching it when Borges, the world number 49 from Portugal, returned into the net.
It preserved Djokovic's winning streak in Beijing, where he has won six titles.