Dinamo had, after all, humiliated Tottenham with a 3-0 win here in March and are aiming to reach the knockouts for a third straight year, in their 16th consecutive season in Europe.
By contrast, this was West Ham’s first ever European group game but the Hammers made light work of their more established rivals, sealing a deserved victory as Michail Antonio and Declan Rice capitalised on loose passes to score either side of half-time.
From the off, it was a savvy, professional away performance in Europe, with goalkeeper Lukasz Fabianski not having a single save to make.
The night represents another impressive step forward for the club under Moyes and suggested the manager, who made five changes from the draw with Southampton, has the squad to compete on multiple fronts this season.
The Hammers immediately go top of their group and should be full of confidence that they can stay there and avoid a potentially tricky play-off for the knockouts.
While West Ham deserved their victory, Dinamo were the makers of their own downfall.
Antonio capitalised on a dreadful back pass from defender Kevin Theopile-Catherine and rounded the goalkeeper to break the deadlock after 22 minutes and Rice’s superb goal also came from a loose pass. The England midfielder drove from the halfway-line, holding off Bruno Petkovic, and fired a low shot between the goalkeeper’s legs.
Moyes was spared the decision over whether to save his only centre-forward for the visit of Manchester United on Sunday by the striker’s late sending off against Southampton, ruling him out of the weekend.
He will be a huge miss after making it five goals in as many games this season at the Stadion Maksimir.
Antonio showed a poacher’s instinct to pounce on Theopile-Catherine’s dreadful pass, skip away from the goalkeeper and finish coolly into an empty net.
He was also cute in flicking the ball round the corner for Ryan Fredericks moments later but the right-back squandered a chance to double West Ham’s lead, firing straight at the goalkeeper.
The more robust side of Antonio’s game was also in evidence, as he kept Dinamo’s centre-backs occupied for long periods, ensuring the Hammers remained on the front foot, even as the hosts enjoyed more possession in the second half.
Top players step up to new challenges and you wonder if playing in Europe will help the likes of Antonio and Rice improve even further and go to a new level.
Kurt Zouma was quietly outstanding on a commanding debut for West Ham, which should set him up for the altogether tougher test of stopping Cristiano Ronaldo and Manchester United on Sunday.
The France international was particularly impressive in the air, towering over Dinamo front two Petkovic and Mislav Orsic – both Croatian internationals – and occasionally stepping out of the defence to meet the ball.
Zouma immediately looked like a new leader for the Hammers and his signing gives Moyes’s side an impressive spine.
The Frenchman can expect to be partnered by Angelo Ogbonna on Sunday and with Rice and Tomas Soucek patrolling the midfield, West Ham will prove a tough nut to crack for even the best sides this season.