The 30-year-old saw the first set slip away from him at the Baku Sports Hall, but he soon bounced back to record a 20-22 21-16 21-13 victory over his Lithuanian opponent.
Abian, who was ranked number one in Europe last year, claims that the first-set error helped him find focus for the remainder of the semi-final clash.
"I made a stupid mistake," he told reporters. "It was 20-18, I came back to 20-20 and then there was a ball which I thought would go out, but it fell in.
"That was stupid judgement mistake, you shouldn't take risks like that at 20-20. After the first set, I changed my mindset. I told myself to forget about it, and play as if the score was still 0-0 in sets."