Motherwell were left to rue missed opportunities after Duk's header gave Aberdeen a first win over them in six attempts.
The Dons twice took the lead through Bojan Miovski and Duk, with the latter also having a strike disallowed for offside.
Aberdeen being clinical with their chances was a crucial difference in this clash, and though Stuart McKinstry scored a fine equaliser, they missed good chances through Kevin van Veen and Blair Spittal.
