Ostapenko got the upper hand over the No 31 seed from Russia, 6-1 3-6 8-6, after an hour 46 minutes, having also defeated Kasatkina in 3 sets in the Eastbourne quarter-finals en route to the title, while Sevastova recovered from a rough start to deny Ukraine’s Kostyuk, 1-6 6-4 6-3, a week after stopping the teenager in the first round at Eastbourne.
Out on No 2 Court, Ostapenko’s blazing hit-or-miss game saw her fall a break down in the final set and, despite Kasatkina serving for the match twice, her irresistible aggression nevertheless carried her through again to the upset win.
The 24-year-old Latvian, who won the French Open in 2017, struck 48 winners and 48 unforced errors in the process.
Kasatkina served for the match at 5-4 in the deciding set, in which neither player could hold serve, but she double-faulted at 30-30 before watching a backhand bullet fly off Ostapenko’s racket and down the line to make it 5-5.
The Russian then led 6-5 only for Ostapenko to drill a forehand winner to level the match again.
The next time Kasatkina served it was to stay alive but she dumped a forehand and Ostapenko celebrated with a huge roar.
The Latvian reached the Wimbledon semi-final after her storming of Paris, but since then she has suffered 5 first-rounds exits at Grand Slams and, from a ranking of 5 in the world, she ended 2019 down at 69 and by 2020 had slumped to 71.
The current World No 34 raced out of the blocks, dominating Kasatkina in a 22-minute opening set, the Russian committing 11 unforced errors, including 4 double-faults, and rarely got her game going, while Ostapenko saved her boldest shots for the biggest points, a searing drive volley to go up 4-1, a vicious return winner for 5-1.
A marvellous lob in the second game of the second en route to capturing Ostapenko’s serve for the first time enabled Kasatkina to gain a foothold in the contest, but the Latvian pulled off 2 clean return winners to break back, 2 forehand winners from defensive positions to hold for 2-2 and 3 consecutive return winners to move up 3-2.
Just when it seemed Ostapenko could do no wrong, her purple patch abruptly came to an end and she was suddenly error-strewn, dropping 5 games in a row to lose the second set and fall behind a break in the third.
The decider was tense and unpredictable, opening with 6 straight service breaks, of which there would ultimately be 11 across its 14 games, and was ultimately decided by a handful of points in Ostapenko’s favour.
Next in the firing line is Australian Ajla Tomljanovic, who beat France’s Alizé Cornet, 6-4 0-6 6-3, in a 2 hour 7 minute see-saw contest.
Earlier, Sevastova had played the reverse role against Kostyuk and, like Kasatkina, the 31-year-old had found herself shut out of a match by her opponent’s aggressive tennis as the Ukrainian pulled off highlight after highlight in a stellar opening set with a drop-shot return, a reflex half-volley winner, crazy sidespin that out-foxed even slice expert Sevastova.
The former US Open semi-finalist is known for her creative shotmaking, but she went back to basics to essay the comeback, improving the effectiveness of her serve.
In the first set, she had landed 52% of her first serves, and won just one of the 11 points behind her second, but those numbers went up as the match went on, reaching 64% in the second, and 57% in the third while, more crucially, she won 19 out of 27 second-serve points in the remainder of the contest.
Kostyuk still had moments of magic to wow the No 4 Court crowd, and seemed to have wrested the momentum back when she pulled off a remarkable drop-shot-lob combination to break Sevastova back for 3-4 in the second set but, serving at 4-5, the Ukrainian threw in several cheap errors to let her opponent off the hook.
The pattern repeated in the decider, in which Sevastova gained an early break, but wobbled to concede it midway through
This time it was her turn to come up with the goods, regaining the break with an exquisite counter-drop and a bold forehand winner, and finally serving out the win on her 3rd match point when Kostyuk sent a forehand long.
Sevastova will next face Roland Garros champion and No 14 seed Barbora Krejcikova as she bids to complete her career set of second-week appearances at every Grand Slam.