The British number one had little trouble disposing of Yulia Beygelzimer, as some good serving set her up for a 6-3 6-2 win over the Ukrainian.
Robson will be hoping for revenge after having lost to the Dane at the French Open earlier this month.
Former world number one Wozniacki also cruised into the last 16 when defending champion Tamira Paszek retired.
The Dane, watched by boyfriend Rory McIlroy, was 6-2 2-2 ahead when the Austrian quit with a leg injury.
The top seed Agnieszka Radwanska is out of the tournament though as she lost 7-6(2) 6-2 to up-and-coming American Jamie Hampton.
On court two, 2011 Wimbledon champion and fourth seed Petra Kvitova swept aside Monica Niculescu 6-4 6-1 despite the Romanian saving a stunning 14 break points.
British wild card and local hope Johanna Konta had no answer to Su-Wei Hsieh, losing 6-4 6-3 to the Taiwan player. British number three Konta is at a career-high ranking of 137 and was a break up in the second set before unravelling.
There was better news for Elena Baltacha as she enjoyed a 7-5 7-6 (7-3) win over Kristyna Pliskova. Baltacha is in good form after having won in Nottingham last week.
2011 French Open champion and second seed Na Li defeated Alize Cornet of France 6-2 6-4 and she will next face former Wimbledon finalist Marion Bartoli next.
2011 US Open champion Sam Stosur found a welcome bit of form as she beat eight seed Nadia Petrova 6-2 6-3 after benefiting from a wild card into the tournament.
In s'Hertogenbosch, Daniela Hantuchova, who was fresh off her first WTA grass court title in Birmingham on Sunday, was forced to retire when trailing Lesia Tsurenko 5-0 in the opening set of their first round encounter.
The Slovak suffered a recurrence of the foot injury she picked up at Edgbaston.
Elsewhere top seed Roberta Vinci beat former Wimbledon quarter-finalist Kaia Kanepi 6-3 6-3.
The powerful Estonian has one of the quickest serves on tour but was broken three times in each set by the Italian.
WTA Eastbourne Round 1 results
Laura Robson (Britain) beat Yuliya Beygelzimer (Ukraine) 6-3 6-2
Ekaterina Makarova (Russia) beat Olga Puchkova (Russia) 6-3 6-0
Samantha Stosur (Australia) beat 8-Nadia Petrova (Russia) 6-2 6-3
2-Li Na (China) beat Alize Cornet (France) 6-2 6-4
3-Angelique Kerber (Germany) beat Sorana Cirstea (Romania) 6-4 6-4
4-Petra Kvitova (Czech Republic) beat Monica Niculescu (Romania) 6-4 6-1
5-Caroline Wozniacki (Denmark) beat Tamira Paszek (Austria) 6-2 2-2 (Paszek retired)
Hsieh Su-Wei (Taiwan) beat Johanna Konta (Britain) 6-4 6-3
Lucie Safarova (Czech Republic) beat Klara Zakopalova (Czech Republic) 6-4 7-6(3)
WTA s'Hertogenbosch Round 2 results
7-Urszula Radwanska (Poland) beat Magdalena Rybarikova (Slovakia) 4-3 (Rybarikova retired)
Tsvetana Pironkova (Bulgaria) beat Irina Begu (Romania) 7-6(7) 6-2
3-Carla Suarez Navarro (Spain) beat Sofia Arvidsson (Sweden) 6-3 6-4
4-Kirsten Flipkens (Belgium) beat Francesca Schiavone (Italy) 3-6 6-3 6-0
1-Roberta Vinci (Italy) beat Kaia Kanepi (Estonia) 6-3 6-3
Lesia Tsurenko (Ukraine) beat Daniela Hantuchova (Slovakia) 5-0 (Hantuchova retired)