The 19-year-old was plucked from the reserves by coach Felix Magath and made his top flight debut last week.
Schalke added a second in first half stoppage time when Rakitic combined with Jefferson Farfan to allow captain Heiko Westermann to fire home from six metres.
Westermann also hit the post with a 20-metre drive as Schalke looked for another goal that would send them joint top.
That came in the 76th minute through Farfan, who had a mediocre first season with them last year, when he started a counter-attack and finished from close range.
Schalke have won both opening Bundesliga matches under Magath, who took over in the close season after steering Wolfsburg to the title.
Wolfsburg are the only other team to have won their first two games. The champions beat Cologne 3-1 on Saturday while Bayern Munich had to settle for their second consecutive draw, 1-1 against Werder Bremen.
Borussia Moenchengladbach scored in each half to beat Hertha Berlin 2-1 and record their first win of the Bundesliga season in Sunday's other game.
Borussia took the lead after 23 minutes through defender Roel Brouwers, who headed in his second goal of the season.
The hosts pushed for a second goal with visitors Hertha relying mainly on long-range efforts.
Borussia netted again seven minutes after the restart when new signing Raul Bobadilla of Argentina combined well with Oliver Neuville, who cut into the box for Karim Matmour to slot home.
Serbian midfielder Gojko Kacar's header cut the deficit one minute later and the same player header against the crossbar two minutes from time.
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