Caroline Wozniacki exited the Stuttgart Open at the first round thanks to a 7-6 6-1 defeat at the hands of Spanish Carla Sanchez.
The Danish star raced into an early lead but was pegged back in the first set, losing the decisive tie-breaker.
World number 27 Suarez then ruthlessly dismantled her struggling counterpart to book her place in the second round.
Jelena Jankovic – who was also once the top-seeded women’s player back in 2008 – enjoyed better fortune against Sam Stosur.
The Serbian won both sets 6-4 in last night’s match and comfortably progressed to the next round.
Speaking to Sky Sports after the contest, she said: “I knew that Sam is a very dangerous opponent, so I am happy to have beaten her.”
“My confidence is coming back and every win helps.”
Jankovic has slipped down the rankings in recent seasons and is currently 18th but there is little doubt that she is capable of competing with the best on her day––
She will play Sabine Lisicki, who hails from Germany, in tonight’s second round clay court match.
Fifth seed Petra Kvitova was more thoroughly tested in her match against wild-card Annika Beck.
The Czech needed three sets to overcome her relatively unknown opponent, and admitted that her performance wasn’t convincing.
“I still don’t feel really good on clay, but it’s getting better,” she said. “It’s better than it was in Katowice, but I want to improve before Madrid.
Elsewhere, Maria Sharapova is set to face Lucie Safarova, while Sara Errani is up against Bethanie Mattek-Sands.