Kartal has enjoyed a remarkable rise through the rankings in the past 18 months.
At Wimbledon last year, she arrived as a wildcard ranked 281 in the world and went on to reach the third round.
On her return this year, ranked 230 places above that, she cut a calm and mature figure.
Ostapenko, 28, had beaten Kartal comfortably in the opening round at Eastbourne last week but the Briton maintained her composure as she fell 5-2 behind in the opening set.
A wayward Ostapenko forehand into the net was the catalyst for Kartal to go on and win the next five games, saving set points at 5-4 before motoring ahead to take the set.
Ostapenko was left stunned when Kartal sent a ripping forehand round the net post but the former Wimbledon semi-finalist managed to cut out the errors and take the second set comfortably to level things up.
That said, Ostapenko grew increasingly frustrated throughout the match – muttering under her breath and berating herself while shouting up at her coaches.
Fans in the crowd were also on the receiving end of glaring looks as she complained that they were being too noisy, asking the umpire to tell them to be quiet before shouting at them and raising her arms in exasperation.
But throughout that Kartal remained steadfast and raced through the third set, securing a double break before serving out for an impressive victory.