Trailing 11-10, Dean Hill tied it at 11:15 of the fourth quarter on a set-up from Mitch McMichael and Duch.
A minute later, after receiving a pass from McMichael, Duch sent a long shot past goaltender Mike Poulin to give Washington the lead for good.
The win moves Washington into a three-way tie for first place in the West with Calgary and Edmonton, who lost to Colorado on Saturday.
Lewis Ratcliff also had three goals for Washington (8-6). Jeff Moleski had a pair while Kyle Buchanan, Mike Grimes and Brett Bucktooth also scored.
Curtis Dickson had three goals to pace the offence for Calgary (8-6). Dane Dobbie and Jeff Shattler had two goals each and adding singles were Dan MacRae, Geoff Snider, Shawn Evans and Scott Ranger.
Goaltender Tyler Richards preserved the win with some great stops in the late going. Two of his 48 stops were dangerous chances late from Dickson and Evans.
The teams were playing the back-end of a back-to-back meeting. Last Saturday, Calgary came from behind with seven goals in the fourth quarter for a 13-11 victory.
Calgary took its third lead of the night with goals 10 seconds apart early in the fourth quarter.
Shattler tied it 10-10 at 4:01. Then, off the ensuring faceoff, Dickson took a nifty behind-the-back pass from Snider and put his team-leading 38th goal past Richards.
Dickson's second goal of the night at 2:54 of the third quarter had helped Calgary open up its biggest lead of the night at 9-5. However, the four-goal margin lasted just 27 seconds.
Ratcliff's power-play goal was the first of five unanswered goals for Washington who stormed back to take a 10-9 lead to the final quarter.
Washington trailed 3-2 after one quarter but Grimes tied the game 40 seconds into the second and Duch gave the Stealth its first lead at 6:27 on the power play.
That lead lasted less than a minute.
Shattler tied it 4-4 at 7:23, which ignited a run of four goals in a row giving the Roughnecks a 7-4 lead at halftime.
Calgary took the lead right off the opening face-off with Snider racing down the floor and scoring after just five seconds, bringing an immediate roar from the energetic Scotiabank Saddledome crowd of 10,008.
Notes: Washington coach Chris Hall, who was the Roughnecks original coach and won a Champion's Cup with them in 2004, coached his 150th NLL game. He is just the fourth coach in NLL history to reach that milestone… Dickson's first goal was his 100th of his career… Dickson is one short-handed goal from matching the NLL single season record of seven. With 12 in his career, he's tied with Tracey Kelusky for the franchise lead… Daryl Veltman (lower body) did not play for the Roughnecks… The Roughnecks are 7-5 against Washington, but just 1-4 at home against them.