Rasmus Hojlund's second-half penalty condemned Wales to their third defeat of the UEFA Nations League, and their second at the hands of Denmark.
The Napoli striker put the visitors ahead from the spot with less than 15 minutes to go after Danny Ward brought down Gustav Isaksen.
Ward had previously made two great saves early in the second half to keep out both Isaksen and Hojlund, but was powerless to prevent the latter scoring his third goal in four international outings.
Bellamy's approach
Bellamy's men produced arguably the most impressive result of his tenure so far by beating Norway on Thursday night, and the Wales boss responded by making one change from the side that saw off Erling Haaland and co, with Brennan Johnson preferred to Daniel James.
Having made six changes for the clash in Copenhagen last weekend, and another five for the win on Thursday, it was a notable change in approach.
Sadly, it didn't quite pay off, with Wales unable to really reproduce the same energy and vigour that had been so successful in seeing off the Norwegians.
First-half chances
The hosts actually made an encouraging start inside the opening 10 minutes, however. Ethan Ampadu lashed over before Johnson fired a volley wide.
Hojlund sent a tame effort into the arms of Ward at the other end, before the visitors were with an early blow, losing Pierre-Emile Hojbjerg to injury.
Isaksen was the scourge of Wales when the two sides met in Copenhagen last week, and he was at the heart of what was perhaps the biggest talking point of the first half after going down in the box following a coming-together with Ben Davies.
Referee Irfan Peljto waved away the Danish appeals, but the visitors continued to grow into the contest, with Morten Hjumland heading wide a few minutes later.
Isaken then sent a crashing effort over high and wide five minutes before the break, before Oliver Provstgaard similarly couldn't keep a header down on the stroke of half-time.
Second-half pressure and the decisive penalty
Ward produced a big save to deny Hojlund from close range early in this second half, as Denmark continue to ask questions of the Welsh defence.
The Wales keeper got down well again to tip Isaksen's header on to the post, with Bellamy responding with a double change in a bid to try and wrestle back some control.
Wales did improve as the game ticked past the hour-mark, with Johnson firing a shot over the bar from a tight angle after some good work down the left from Sorba Thomas.
The hosts looked to be heading for what would have been their first clean sheet since November, but laboured to open up the Danish defence.
But their efforts took a hammerblow on 75 minutes as Ward clattered into Isaksen after misjudging a pass, and Hojlund rolled the subsequent penalty into the net - a goal that would ultimately seal what was probably a deserved victory for Brian Riemer's side.
Wales remain on three points in the group, with a home clash with Portugal and an away trip to Norway to come in November.
