As United pursued the winner, Cavani peeled away to meet Rashford's cross and beat McCarthy in the second minute of stoppage time.
The three points lifted United to ninth in the Premier League, seven points off leader Tottenham.
He made 184 appearances for the Reds, scoring 56 goals, before moving on to Oldham Athletic in 1964.
The 25th-minute equalizer arrived when left back Luke Shaw had time and space to send over a cross that was met with a header from Fernandes from 12 yards (meters).
Unlike PSG and United, Barcelona and Juventus look well set to advance from their Group G.
Drawn in one of the toughest Champions League groups alongside two teams who reached the semifinals last season, United has consigned star-studded Paris Saint-Germain to a first group-stage home loss in 16 years and handed Leipzig — the-then German league leader — the heaviest defeat (5-0) in its 11-year history.
Arsenal hadn't beaten United away since an FA Cup game in 2015, part of a longstanding run of poor form for the Gunners when facing England's biggest clubs on the road.
The announcement came two days after Nobby Stiles, who won the 1966 World Cup and 1968 European Cup as Charlton's teammate, died after his own battle with the illness.
Telles had joined United on deadline day earlier this month and made an impressive debut for the Reds in last week's 2-1 victory over Paris Saint-Germain.
On Thursday, Rashford had urged local businesses to tweet using the hashtag #endchildfoodpoverty, which would allow the 22-year-old to locate them.
Manchester United were held to a goalless draw by Chelsea at Old Trafford, as the Reds remain winless at home for three matches in a row since the season began.
The 22-year-old England international successfully lobbied British Prime Minister Boris Johnson's government in June to extend free school meals through the summer.
The Premier League club, which is listed on the New York Stock Exchange, generated 509 million pounds ($665 million) in the year to June 30 — a drop of 19%
Marcus Rashford scored the winning goal in the 87th minute as Manchester United defeated PSG 2-1 in the Champions League.
Live Streaming Champions League Paris Saint-Germain vs Manchester United: Here are the details of when and where to watch PSG vs MAN U live football match online.
Paris Saint-Germain hosts Manchester United for one of the standout games of the opening round. They met in the last 16 two seasons ago, when United advanced in dramatic fashion thanks to a stoppage-time penalty winner in the second leg in Paris.
The Uruguay striker seemingly wants the world to know he is in good shape and ready to make his debut for Manchester United.
The 29-year-old Welbeck was available on a free transfer following the expiration of his contract at Watford where he scored three goals in 20 appearances last season as the team was relegated from the Premier League.
Bruno Fernandes made amends after missing the penalty as the side put four past Newcastle in a late comeback on Saturday.
The plans were publicly announced and backed Sunday by the chairman of the English Football League, Rick Parry, who runs the competition featuring the 72 professional teams below the Premier League.
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