“It was a bit of a blur,” he told BBC Sport. “I threw in a dodgy service game at 5-4 and I felt like I was there in the tiebreak but I was 8-4 down.
“He threw in a double [fault] at 8-4, and I was like ‘okay, he’s feeling it’, so I continued to gets balls in court and to be aggressive and somehow won.”
One of four British players granted wild cards into Wimbledon pre-qualifying, Stewart has now won four matches at Roehampton.
“It’s been a rollercoaster,” he added. “I’ve had a bit of luck but I feel I was due a bit of luck and I’m loving the experience.”
Riedi, 23, reached the last 32 by upsetting Argentine 24th seed Federico Agustin Gomez, again in a deciding tiebreak.
Wimbledon begins on 30 June, with Scotland’s Jacob Fearnley and Cameron Norrie already in the main draw.
