Group A: Shakhtar Donetsk 1 Manchester United 1
Moyes can do with all the little snippets of posivitity he can lay his hands on just now.
And, with Arsenal (twice), Tottenham Hotspur and, last season, Chelsea all beaten here, Moyes can look back with some satisfaction on a result which consolidates a decent start to Group A.
Yet the Scot may also lament the fact his side got within 15 minutes of what would have been an impressive victory.
Scorer of United's last away goal in the competition, against Real Madrid, Danny Welbeck was on the mark again, steering home after Yaroslav Rakitskiy had made a hash of clearing Marouane Fellaini's low cross.
It was Welbeck's third goal of the campaign, one more than he managed in the whole of last season, and for a good while afterwards seemed set to prove the difference.
But Shakhtar continued to press and when Taison thrashed home an impressive effort, United needed all its battling qualities to gain the draw its industry deserved.
Beleaguered on the home front, confident in foreign lands.
If Moyes has had his struggles trying to work out the merits of his United players, the club's supporters are equally baffled as to the balance of the season as a whole.
Currently in the wrong half of the Premier League table after three defeats in its opening six games, its worst start since 1989, the backdrop to a trip to Donetsk was as bleak as the weather in this mining city.
Until Juventus came to the Donbass Arena and won in December, Shakhtar had pieced together an impressive 49-game unbeaten run on home soil.
So, after the 10 days he has endured, to reach half-time a goal up and with his defence holding reasonably firm, Moyes had every right to regard it as some kind of success.
United was more impressive for the fact Wayne Rooney was missing after suffering a shin injury in training before he had even left England which had swollen up overnight.
The visitor was not entirely perfect.
Tom Cleverley got away with a sliding penalty area challenge on Alex Teixeira which got the faintest of touches to the Shakhtar man, but enough to offer the opportunity of an exaggerated fall, looking for a penalty.
Thankfully for Cleverley, referee Pavel Kralovec was unsympathetic to Teixeira's plea.
Robin van Persie curled over after a neat control and turn onto Cleverley's pass before Welbeck put the visitor ahead.
Yaroslav Rakitskiy will not look back on the goal with any fondness, virtually teeing Welbeck up as he tried to intercept Fellaini's cross.
The England striker needed no second invitation though and drilled his first-time finish into the bottom corner.
Shakhtar dominated possession for long periods thereafter.
However, Nemanja Vidic had one of those nights which confirms his status as a central component of Moyes's squad.
Always in the right place to make a block or decisive intervention, the Serbia star's defensive instincts are such that any concerns about his dodgy knees will surely be overlooked when discussions begin over an extension to the contract which expires at the end of the season.
Taison did get past Rafael to fizz a low cross into the area which David de Gea, one of only two survivors from last weekend's home defeat by West Bromwich Albion, got down bravely to smother.
It was also Taison who belted a free-kick into the wall after Vidic had been booked for upending Luiz Adriano.
The introduction of Ryan Giggs for a record 145th Champions League appearance - including qualifiers - was supposed to shore United's defence up for the final assault.
Instead, it was followed within minutes by Shakhtar's equaliser as Vidic could only turn Rakitskiy's cross into the path of Taison, who blasted home.
United creaked a couple of times after that. But it was never in serious danger of being overhauled.