With group rivals Poland taking an early lead against Montenegro, the Danes knew that they could no longer win the group, but Bendtner and Pione Sisto were keen to give the sell-out crowd at the Parken Stadium their money's worth.
Sisto let fly with a stinging shot from distance on the half-hour mark that was touched over the bar for a corner, and moments later Bendtner missed a glorious chance to put Denmark in front as his shot was blocked by a last-ditch tackle.
Shortly after, the 29-year-old former Arsenal and Juventus striker had the ball in the net, but the goal was disallowed for offside.
Bendtner finally paved the way for the deadlock to be broken when he was pulled back in the box on the hour mark by defender Cristian Ganea as he attempted a header, and Christian Eriksen stepped up to convert the spot kick.
Ganea was sent off moments later, collecting his second yellow card for dragging down Yussuf Poulsen, but despite being down to ten men, Ciprian Deac fired home a late equaliser for Romania in the 88th minute.
Poland beat Montenegro 4-2 to finish top of Group E on 25 points with the Danes second on 20, four ahead of third-placed Montenegro and seven ahead of Romania, who finished fourth.
(Reporting by Philip O'Connor in Stockholm; Editing by Christian Radnedge)
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