In the tournament's first match on Arthur Ashe, Radwanska needed just 63 minutes to wrap up a relatively straightforward 61 62 win.
The only slight wobble for Radwanska came at the start of the second set when she slipped 2-0 behind. However, unflappable as ever, the Pole hit back immediately before earning the chance to move a break ahead herself after outmaneuvering Soler-Espinosa in characteristically well-constructed point.
She snapped up the chance at the first time of asking with a slightly less characteristic bludgeoned return winner, wrapping up the win a few moments later with a precise serve out wide.
"The first match is always tough and it takes some time to get used to the conditions," Radwanska said in her on-court interview. "I'm just very happy that I could play my best tennis and get a win on Ashe on the first day!
"Today was really windy and it made it difficult when we changed sides. But I think I used the wind well today and I'm pleased I could close it out in straight sets."
Li has only once been beyond the fourth round in eight previous visits to Flushing Meadows but looked in good nick during the tune-up events in Toronto and Cincinnati, reaching the semifinals of both occasions.
She continued in this rich vein of form against Govortsova, hitting 28 winners - and just 13 unforced errors - during their hour on court.
"The first match at a major is always a tough match because you never know what will happen on the court. It's just important to get the win," Li said. "My form has been pretty good this summer - I had two semis and I was really happy with the way I was hitting the ball now on the court.
"I just want to continue playing like this, keep trying my best and hopefully go far in the tournament."