World number 64 Tomic has endured a difficult season and was forced to retire from the French Open at the first round stage with a hamstring injury but was rarely stretched in what was a first meeting between the players.
Tomic broke the serve of world number 216 Ward to take a 5-3 advantage in the first set before holding to confirm the set, and it was a similar story in the second as it went with serve until the Australian secured a late break to wrap up the win in just over an hour.
The win was Tomic's first match in almost two months - his first since his father, John, was charged with allegedly assaulting Bernard's former training partner, Frenchman Thomas Drouet, in May.
ATP Eastbourne results
Julien Benneteau (France) beat 5-Kevin Anderson (South Africa) 7-6(4) 6-2
Radek Stepanek (Czech Republic) beat Marinko Matosevic (Australia) 6-3 6-2
Ivan Dodig (Croatia) beat Denis Istomin (Uzbekistan) 6-3 6-4
Martin Klizan (Slovakia) beat Viktor Troicki (Serbia) 6-3 6-2
Bernard Tomic (Australia) beat James Ward (Britain) 6-3 6-4
Feliciano Lopez (Spain) beat Jarkko Nieminen (Finland) 7-6(3) 7-6(5)