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.
'Tough match'
Earlier, Karen Khachanov swept aside second seed Felix Auger-Aliassime 6-3, 6-3 in their first-round meeting.
Khachanov, the world number 26, won three straight games, taking the first set in 31 minutes.
The 30-year-old then kept his cool to break Auger-Aliassime on the first match point, wrapping things up in one hour and 11 minutes.
He faces either Arthur Rinderknech of France or qualifier Alex Molcan of Slovakia in the round of 16.
Khachanov brushed off suggestions that he had Auger-Aliassime's card marked following his second statement win over the Canadian world number five in a matter of weeks.
"It was a tough match," the Russian, who triumphed at the US Open, said.
"When you approach this match, you are thinking it's a completely new match, completely different. In China, in Beijing. Different court, different balls.
"You just focus again from zero. You know what you did well... and you just try to keep the momentum going. There is not much secret about it."
World number two Alexander Zverev, fresh off a US Open win and the top seed in Beijing, was scheduled to start his bid against Cameron Norrie in the first round on Thursday.
While the battle for world number one has been on his mind, the 29-year-old German told reporters Wednesday that his focus was still to "do everything I can to prepare myself to play good tennis".
"Everything else will fall into place," he said.
A 1000-level WTA event is also taking place in Beijing.