Todd Cantwell's stunning second-half volley was enough to help Rangers to a 1-0 win over Aberdeen at Ibrox.
The visitors should have taken a lead into half-time after Duk was presented with two glorious chances by some lapse Rangers defending, but the forward saw his first effort saved and clipped the second over the bar.
News of Celtic retaining their title with victory at Hearts filtered through to the Rangers fans at the start of the second half, which contributed to a muted atmosphere.
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But Cantwell woke the home fans from their stupor when he met James Tavernier's deep corner with a brilliant far-post volley, ensuring the blue half of Glasgow had something to cheer on a day in which their rivals will dominate the headlines.
McCrorie helps Rangers to tight win
Michael Beale spoke of an impending rebuild in the wake of Rangers’ Scottish Cup semi-final defeat to Celtic last weekend, and the manager wielded the axe for the visit of Aberdeen by making five changes.
Robby McCrorie replacing Allan McGregor to make his first Premiership start of the season was the most eye-catching of the changes, but the goalkeeper justified Beale’s faith with an impressive performance.
McCrorie’s first save of note saw him deny Duk, who was forced wide by Bojan Miovski’s disappointing pass but still managed to force the Rangers goalkeeper into a smart save at his near post.
Duk then wasted another chance when he raced clear into Rangers’ half only to chip his effort onto the roof of the net, but not before Kelle Roos denied Fashion Sakala from close range in the opposite penalty area.
Jonny Hayes nearly handed Rangers the opening goal when he shanked a clearance onto his own crossbar shortly after half-time, before McCrorie was called into action again to tip Matthew Pollock’s header over.
Cantwell then provided the game’s standout moment with his fourth goal for Rangers, with Scott Wright and Tavernier then going close to sealing victory.
Shayden Morris had Aberdeen’s final chance of the game but was again denied by McCrorie.
Beale: We've not performed on biggest occasions
Michael Beale congratulated Celtic on another title and admitted Rangers will "assess and be honest in our feedback" as they bid to bring the title trophy back to Ibrox next season.
"The table doesn't lie," said Beale. "Our league form's been outstanding since November but we've not been able to get close to them, so credit to them.
"It's important we come back next year and make a bigger challenge. I think at both ends of the pitch they've been a bit more decisive, and in the one-off games they've found a way to beat us.
"It doesn't taste too good but we have to assess and be honest in our feedback in terms of recruitment and the improvements we need to make.
"In the league, in the main, I've been pleased, but on the big days this team's failed to get the results we're all craving."
Beale also revealed Robby McCrorie will continue to keep Allan McGregor out of the side for the time being, saying: "I think, at this moment in time, Robby will continue.
"I'm not saying he'll play every game. Robby will have to perform, like everyone else."
Robson: We missed two of the best chances you'll ever see
Aberdeen boss Barry Robson was not happy to see his side's seven-game winning run come to an end, but felt his side were unlucky not to take points off Rangers.
"We missed two of the best chances you'll ever see in the game in the first half and Morris had a really good chance in the second half," Robson said.
"It's hard to deal with their movement and rotations at times but I thought we did quite well. On another day we could have come away without defeat.
"I'm not happy because we didn't win the game but it's hard for other teams with the Old Firm's might and their finances, and their ability to control matches.
"But what you can do is control them in another way and we did that today. At times we could have been a bit better with the ball but we tried to cut them open quickly."
What's next?
Rangers' next Scottish Premiership game is at home to Celtic on Saturday, live on Sky Sports - kick-off 12.30pm.
Aberdeen host Hibernian on the same day, with the game kicking off at 3pm.