Having initially brought the hosts level in the first half, Bendtner stole the headlines when he struck twice in the closing minutes to seal a hard-earned victory, giving captain Christian Eriksen something to celebrate on his 50th international appearance.
Jozy Altidore had earlier given the US the lead in the first half, but the Bendtner show began 12 minutes before the break when he converted from close range.
Despite controlling the game for long spells, Morten Olsen's side were punished again just after the hour mark, as Aron Johannsson tapped home.
However, it was not enough as Bendtner scored a late brace to deny USA a win that would have boosted their CONCACAF Gold Cup preparations.
With Eriksen leading Denmark on his landmark appearance in the absence of Daniel Agger, the hosts made a promising start, with Lasse Vibe particularly impressive down the right.
The Gothenburg forward delivered two threatening crosses into the USA penalty area early on, but John Brooks and Michael Orozco were on hand to clear the danger.
Denmark's control of proceedings quickly disappeared in the 19th minute, though, as a swift attack from the visitors saw Altidore net his 27th international goal.
Having muscled his way past Daniel Wass and Simon Kjaer to meet Timothy Chandler's long diagonal cross, the Toronto striker thumped a left-foot volley beyond Stephan Andersen from a tight angle.
Three minutes after the half hour, Denmark pegged the visitors back with a well-worked move, Bendtner converting from close range after Vibe had flicked on Wass' low cross.
Vibe was at the heart of all the positive play from the hosts in the opening 45 minutes, and they should have gone into the break ahead as he put a low cross into the path of Bendtner, but the Wolfsburg striker was unable to double his tally.
Denmark kept up their fast pace after the restart and saw another two chances go begging before the hour – Bendtner and Vibe both volleying wide from inside the penalty area when well placed.
In an almost carbon copy of the first half, Denmark were then made to pay for their profligacy as USA took the lead for a second time through Johannsson, the 24-year-old tapping home Altidore's pass after 66 minutes.
That appeared likely to be enough as Johannsson's goal looked decisive, but with time running out Bendtner returned to fire low past Nick Rimando to level things for a second time.
And the former Arsenal striker was not finished there, as deep into stoppage time he expertly converted a volley from 15 yards into the bottom corner to snatch victory for the Danes.
There was still time for Brooks to waste a glorious chance to earn a draw with a late header when unmarked, the Hertha Berlin defender inexplicably nodding wide having lost his covering defender.
