Leonardo Mayer saved seven of nine break points against Gilles Simon on Tuesday to book his place in the Nature Valley International second round.
Simon – a runner-up at Eastbourne in 2013 – put his Argentine rival's serve under immense pressure throughout their clash, but was unable to find enough momentum to keep his latest title challenge alive.
Finding a way through was no easier for fifth seed Mayer, but when he did it was at opportune times as he completed a 6-4 7-6 (7-4) win in one hour and 50 minutes.
Things were much quicker for Steve Johnson as he accounted for Daniil Medvedev, while the American's next opponent Mischa Zverev had to come from a set down to oust Nicolas Jarry.
Tuesday also saw wins for Mikhail Kukushkin and Lukas Lacko, with Cameron Norrie giving the home fans something to cheer with a late victory over Daniel Brands.
In Turkey, Jiri Vesely booked his third quarter-final of the season as he beat Fernando Verdasco 6-3 7-5 at the Antalya Open.
Mikhail Youzhny was unable to move closer to a 500th Tour win, though, as Robin Haase progressed from their delayed match from Monday.
As a result, Youzhny remains three shy of becoming the second Russian after Yevgeny Kafelnikov to reach the milestone.