Kasatkina, the Australian No.2, won 6-7 (5-7) 6-1 6-4 to become the first Australian into the third round of the grasscourt slam.
Osaka, who beat Anastasia Gasanova 6-3 6-2, may appear a daunting opponent as a four-time grand slam champion, but the former world No.1 has never gone beyond this stage at Wimbledon.
Nor has Kasatkina, but if she can reproduce the form she showed in the middle set against Tjen she has a real chance.
Opening up on court 16, one of the quartet of tight outside courts squeezed between the Centre Court and Court No.1, Kasatkina began slowly and found herself 2-4 down.
She broke back to level the set. She then saved three set points at 4-5 before going into a tie-break, at which point her powers of recovery ran out.
The 29-year-old took a 5-1 lead but a failed drop shot at the net was followed by an unlucky net cord and double fault. That handed Tjen a set point the Indonesian took with aplomb.
Kasatkina, currently ranked No.65 and 23 places below her opponent, shook off this collapse to assert herself in the second set by rattling through it in 31 minutes, playing with aggression and confidence.
Tjen, making her Wimbledon debut and seeking to reach the third round of a grand slam for the first time, took a toilet break but that did not initially change the pattern as Kasatkina secured an early break.
However, the 24-year-old from Jakarta broke back. Kasatkina broke again to lead 4-3, but Tjen once more responded. But this time Kasatkina saved the break before acing the 14th point of the game.
Tjen, who became the first Indonesian to win a match at Wimbledon since 2003 when she beat 2019 US Open finalist Leylah Fernandez in the first round, did not surrender easily.
Backed by a small but noisy band of supporters, she held to 4-5 then saved two match points before Kasatkina's double fault handed her a break point.
But the new Aussie saved that, forced a third match point and won it with a powerful unreturned serve.
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