An inauspicious start saw Jovanovski lose eight of the first nine points to fall an early break behind. But she soon snapped out of this slumber, five games on the trot getting her back on track and on the way to the opening set.
The No.5 seed continued this dominance in the second, breaking twice more to run out a 6-3, 6-1 winner.
Since turning professional in 2007, Eguchi has plied her trade exclusively on the ITF Circuit, but, judging by the performances on her WTA main draw debut, she is clearly intent on making up for lost time.
Despite the one-sided scoreline, Eguchi did not have things all her own way. The first four games lasted nearly half an hour, during which time Eguchi was forced to fend off a succession of break points. Once through this test, Radwanska's challenge began to fade and Eguchi eased to her 31st win of the season.