Swiatek has won four titles on the clay at the French Open, as well as the US Open in 2022, but has struggled on the lawns of the All England Club.
Her previous best result at Wimbledon was a run to the quarter-finals in 2023.
Swiatek broke her opponent twice in the opening set to take a firm grip on the match, benefiting from a flurry of unforced errors from her opponent and winning 100 per cent of her points on first serve.
Two double faults from Russian 19th seed Samsonova handed Swiatek an early break in the second set and she snuffed out a clutch of break-points in the following game to go 3-0 up.
The 24-year-old was pegged back by two breaks of serve as her level dipped and Samsonova pulled level at 4-4.
But Swiatek regrouped and broke again to seal the win.
"It feels great. Even though I'm in the middle of the tournament I've already got goosebumps after this win. I'm super happy and super proud of myself and I'll keep going," she said.
"Honestly, I've really enjoyed playing this year and hopefully it's going to last as long as possible.
"For sure I feel like I really worked hard to progress here on this surface."
The former world number one has gone under the radar at this year's Wimbledon as most of the other top women's seeds have tumbled, though world number one Aryna Sabalenka is still standing.
After slipping down the rankings, she is now back in the world's top four having reaching the Bad Homburg final on grass last month.
The former Wimbledon junior champion lost in the semi-finals of both the Australian Open and the French Open this year.