The British number two has only once failed to make the last 32 when he has been in the main draw and progressed to the fourth round 12 months ago.
Having lost only six games to Jiri Vesely in the first round, Evans looked set for another comfortable afternoon against Australian Duckworth when he eased into a two-set lead.
But Duckworth, ranked 83rd, took his first break point of the match in the ninth game of the third set and then had an early break in the fourth before Evans fought back to clinch a 6-3 6-2 4-6 6-4 victory.
The 20th seed did not hide his delight at the end, spreading his arms wide and running to the net after taking his first match point with a backhand pass threaded down the line.
Evans said: “It was getting difficult. I was in control and then I thought he played very well to get back in.
“I was just happy to get off, really. It was nice to win that match to get to the third round. It’s a match I’m on paper supposed to win. It was my goal to get to where I needed to get to in the seeding spots, do my job, and then go from there.”
Evans had a lot of support, including from Tim Henman, who was watching courtside.
The pair have very similar game styles, and Evans said: “I speak to him quite often. He’s obviously a reassuring figure to have by the side of the court. He’s close probably to getting me a coaching fine pretty quickly.”
Evans will now take on former champion Marin Cilic for a place in the last 16.