Ward will make his Wimbledon debut this year
James Ward and Josh Goodall won their first ATP Tour matches and were joined in the second round at Eastbourne by fellow Briton Alex Bogdanovic.
Ward, 22, triumphed 6-1 6-3 against Victor Crivoi, a Romanian ranked 137 places above him.
British number two Bogdanovic defeated Ivo Minar 6-4 7-6 (7-3) to record his first ATP Tour win of the season while Goodall thrashed Tatsuma Ito 6-4 6-1.
All three British players have both been awarded Wimbledon wildcards.
Ward could meet top seed Igor Andreev in the next round in Eastbourne if the Russian gets past Canadian qualifier Frank Dancevic.
"I've been looking forward to this tournament for a while and obviously getting a wildcard was great," said Ward.
"I went out there today and played well and that will stand me in good stead for Wimbledon next week."
Bogdanovic, who came through qualifying to reach the main draw, will play second seed Dmitry Tursunov in the second round at Eastbourne.
"Dmitry is a strong guy, he's got big weapons," said Bogdanovic.
"He's definitely tough but I've just got to go out there and play the way I've been playing."
Colin Fleming failed to follow in his compatriots' footsteps, losing 7-6 (7-2) 1-6 6-3 to Yen-Hsun Lu of Chinese Taipei in the first round.