The former British number one has dropped down the rankings after taking eight months out to have foot surgery following the Olympics, but won her first trophy of the year last week in Nottingham.
The 29-year-old loves grass and proved the stronger at the end of both sets in Eastbourne, recovering from having her serve broken when she served for the match to win the second-set tie-break.
However, British number three Konta, at a career-high ranking of 137, bowed out.
She had extra reason to want to do well given Eastbourne has been home since her family moved to Britain from Australia eight years ago, but she found world number 44 Hsieh Su-wei too tough.
Konta fought back from 4-2 down in the first set and had an early break in the second, but she was always under pressure and went down 6-4 6-3.
Former world number one Caroline Wozniacki was watched by boyfriend Rory McIlroy, who headed straight to Eastbourne from the US Open golf.
And the Danish fifth seed managed only her second win in eight matches, albeit by retirement, with defending champion Tamira Paszek quitting with a leg injury trailing 6-2 2-2.
Paszek beat Wozniacki in the opening round at Wimbledon last year before going on to reach the quarter-finals but has had a miserable 2013, winning just two matches.
Third seed Angelique Kerber is through to round two, the German beating Romania's Sorana Cirstea 6-4 6-4, while, fourth seed and former Wimbledon champion Petra Kvitova was a comfortable 6-4 6-1 victory over Monica Niculescu.