Jose Mourinho's men attracted plenty of admirers for their impressive start to the campaign, but they were not at their best in front of goal and Choupo-Moting inspired Stoke to a commendable point at the bet365 Stadium.
An entertaining first half saw both sides look a danger going forward, with United in particular guilty of wasting numerous chances to take the lead.
Eventually Stoke found the breakthrough in the 43rd minute through Choupo-Moting, but that only seemed to jolt United into life, as they restored parity shortly after in fortuitous circumstances when a Paul Pogba header deflected in off Marcus Rashford.
Romelu Lukaku put United ahead for the first time just before the hour, but like with Stoke's opener, an equaliser followed soon after as Choupo-Moting doubled his tally.
United looked the more likely to steal a late winner, but Stoke defended valiantly and kept United's frontline at bay.
Stoke started the brighter of the teams and threatened twice in the opening 10 minutes, with Choupo-Moting and Jese Rodriguez both getting in behind the defence and going close.
United soon woke up and troubled their opposition in a similar fashion, as Lukaku latched on to Rashford's pass and crossed towards Pogba, whose back-heeled effort was deflected behind.
The home side struggled to deal with the lively Rashford and he went close twice in quick succession just before the half-hour mark.
His first opportunity saw the forward race on to a through ball and test Jack Butland from 16 yards, before forcing an even better stop from the goalkeeper with a controlled effort which looked destined for the bottom-right corner.
Stoke took full advantage of those let-offs late in the half – Choupo-Moting slamming in from close range after a fine Mame Biram Diouf cross.
Their joy was short-lived, though, as United levelled a few moments later as Pogba's header hit an oblivious Rashford following a Henrikh Mkhitaryan corner and found the net.
United completed the turnaround in the 57th minute and Mkhitaryan was at the centre of things again, slicing open the Stoke defence with an intricate pass for Lukaku, who found the net at the second time of asking after Butland saved his first effort.
But Stoke were level again shortly after.
David De Gea made a remarkable save to deny Jese initially, but from the resulting corner he was rendered helpless, as Choupo-Moting headed in at the back post after shaking off Phil Jones' weak challenge.
There was still time for United to almost snatch it with two late chances.
The first fell to Lukaku, who inexplicably turned Antonio Valencia's cross over from eight yards with nine minutes left, before Butland heroically got down to prevent Kurt Zouma from scoring an own goal deep into stoppage time.
Key Opta stats:
- Manchester United haven’t won any of their five Premier League away games at Stoke since Sir Alex Ferguson retired in 2013 (D3 L2) – only at Chelsea, Tottenham (4 each) and Cardiff (once) have they failed to win in the league since the Scotsman left.
- Eric Maxim Choupo-Moting’s opener was the first goal Manchester United had conceded in 535 minutes of Premier League football, since Harry Kane’s strike at White Hart Lane in May.
- There were just 161 seconds between Choupo-Moting’s opener and Marcus Rashford’s equaliser for Man Utd.
- Only Wayne Rooney (15) scored more Premier League goals as a teenager for Man Utd than Rashford has (currently 12, same as Ryan Giggs).
- Romelu Lukaku’s strike was his 150th in club football (41 Anderlecht, 17 West Brom, 87 Everton and 5 for Manchester United).
- No player has scored more goals in their first four Premier League games for Man Utd than Lukaku (4, same as Louis Saha, Robin van Persie and Zlatan Ibrahimovic).
- Choupo-Moting became the first player to open his Premier League goal account with a brace against Manchester United since Afonso Alves in April 2008.
- Mark Hughes has become only the second manager to go unbeaten in four consecutive Premier League managerial clashes with Jose Mourinho, after Ronald Koeman (5 games).