Bedene threatened to stage a fightback in the second set before Istomin, who won his first ATP Tour title in Nottingham in June, sealed a 6-3, 6-3 victory in 71 minutes.
After saving two break points to level at 2-2 in the opening set, Bedene was unable to repeat the trick in his next service game and Istomin comfortably closed out the set after 38 minutes.
Bedene, who at 50th in the world is ranked three places above his opponent, lost his serve in the opening game of the second set and also in the fifth as he fell 5-1 behind before reclaiming one of the breaks as Istomin served for the match.
However, the Slovenia-born 26-year-old then squandered three game points and eventually lost his serve for the fourth time in the contest as Istomin advanced to a second-round clash with top seed Marin Cilic.
Meanwhile, top seed David Ferrer overcame a poor start to beat fellow Spaniard Albert Ramos-Vinolas in the first round of the Erste Bank Open in Vienna.
Ferrer dropped the first set 6-1 but recovered to win the second 6-3 and took the decider 6-4 to progress in an hour and 53 minutes.
Third seed John Isner needed two tie-breaks to advance to the second round, beating Kenny De Schepper 7-6 (7/4), 7-6 (7/5).
Isner powered down 16 aces and did not face a break point in the entire match, which lasted almost one and three-quarter hours, against the 123-ranked Frenchman.
There was better news for France’s Gael Monfils, who overcame Brazil’s Thomas Bellucci 6-7 (5/7), 6-3, 6-4.
The sixth seed was in action for the first time since retiring in the first round of the US Open with a back injury and he was out on court for two-and-a-half hours.
Elsewhere, unseeded Italian Paolo Lorenzi defeated Rajeev Ram 6-7 (4-7), 6-1, 6-4, Sergiy Stakhovsky beat Jan-Lennard Struff 6-4 6-4 and Steve Johnson got past Alexandr Dolgopolov 6-3, 4-6,