After making heavy weather of Marina Erakovic in her opening match, Kvitova was forced to dig deep once again, eventually negotiating her way past the stubborn Spaniard, 6-7(4), 6-4, 6-2.
Soler-Espinosa has endured a difficult first half of 2015, winning only one match heading into the tournament. However, if she was lacking in confidence it was not evident against the No.4 seed as she recovered from a shaky start to pinch the opening set on a tie-break.
Both players struggled to control their nerves - and unforced error count - in the second. In the end, it was Kvitova that managed them better, breaking in the ninth game before rifling winners off each wing to level the match up.
With Kvitova's forehand now beginning to find its mark, it was not long before she got her nose in front in the decider, breaking for a 3-2 lead. A few games later she arrived at match point, delivering the knockout blow with her 46th winner of the match.
Unfortunately for the Czech, there were also 56 unforced errors, a number she will need to lower considerably when she takes on Irina-Camelia Begu in the next round.
Kvitova's only previous meeting with Begu came just a few weeks ago during her run to the title in Madrid. On that day, Kvitova prevailed in two tight sets and, judging by Begu's performance in her 6-2, 6-0 second round win over WTA Rising Star Ana Konjuh, another hard-fought encounter could be on the cards.