Swiatek suffered a second-set wobble that left her in danger of becoming only the third reigning female Wimbledon champion to lose in the first round in the Open era.
But world number three Swiatek, a six-time Grand Slam champion, steadied her nerves in the deciding set, surviving a 21-minute first game before securing the breaks of serve that edged her into the second round.
The visibly emotional Swiatek buried her head in a towel after converting match point.
The 25-year-old Pole hasn't reached the semi-finals of a Grand Slam in her last three attempts since winning Wimbledon.
Townsend's power-hitting pushed Swiatek to the brink of another disappointment at the majors.
But the 30-year-old has never been past the Wimbledon second round and Swiatek did just enough to set up a last-64 clash against 2021 Wimbledon runner-up Karolina Pliskova.
"It was a tough couple of weeks. A season when not everything went how I wanted. I don't think I won any three-set matches this year, so I'm happy I could do it," Swiatek said.
"Obviously it means a lot to be the defending champion here. In the end I kept my composure. I knew I needed to be solid."