The former finalist came under pressure early on from the world number 22, but was able to save a couple of break points.
However, the Russian continued to push, and edged ahead when a number of errors from the fourth seed allowed her to secure a break of serve before serving out the first set 6-3.
Makarova dominated the second set, preventing Radwanska from claiming a single game before rain interrupted play as the Polish player was about to serve to stay in the match.
Trailing 5-0 when play resumed this evening, Radwanska was unable to find her form on serve, allowing Makarova to wrap up the second set 6-0 and the match after less than an hour total playing time.
Makarova will play the Czech Republic's Lucie Safarova in the quarter-finals.