The seventh seed looked impressive on a breezy Court Three as he posted a 6-3 7-5 6-4 victory.
Rublev is one of 17 Russian and Belarusian players in the men's and women's singles draws after they were banned in 2022 following Russia's invasion of Ukraine, which Moscow calls a 'special military operation'.
He was joined by Belarusian former world number one Victoria Azarenka (33) as the women's 19th seed edged past China's Yuan Yue (24) 6-4 5-7 6-4 and there was also a win for Russian 12th seed Veronika Kudermetova (26) who beat Estonian veteran Kaia Kanepi (38).
Wimbledon was the only one of the four Grand Slam tournaments to ban Russian and Belarusian players last year - a decision that resulted in ranking points being taken away from the event by the ATP and WTA Tours.
As part of their return, players from the two nations are playing as neutrals and must sign personal declarations pledging not to support Russian President Vladimir Putin's regime.
Players are not allowed to receive state funding or have sponsorship from Russian or Belarusian companies.
Wimbledon's U-turn, confirmed by All England Club organisers in March, attracted some criticism with Ukraine's Foreign Minister Dmytro Kuleba calling the decision "immoral".
WARM WELCOME
Rublev, who wrote "No War" on a camera lens at a tournament shortly after Russia invaded Ukraine in February 2022, was given a warm welcome by the crowd on a breezy Court Three.
He looked comfortable on the grass as he proved a class above 64th-ranked Purcell to reach the second round.
"I feel really happy to be back, because in general I didn't play much Wimbledon or I was injured or was pandemic or then they ban us," Rublev told reporters.
"So, of course, really special and really happy to be back in London to play at one of the best tournaments and to get a win today was a nice moment."
Asked about Wimbledon's ban last year, Rublev, who reached the fourth round in 2021, added: "If we really want to help or do what is better for tennis and for the people, I think obviously there were better options.
"Because in the end, there was no difference. They did only worse to themselves. For sure there were options for everyone. Now we are here and I'm really happy to be back and to compete."
Kudermetova said she had received a good reaction from the crowd.
"They support. I think it doesn't matter from which country you are, we are here just a tennis player, we are here to compete and try to show our best," she said.
