Aberdeen, who are second in the Premiership, won that clash at Tynecastle 4-0 in January to set up a final next Sunday against Inverness.
And St Johnstone, who are four places lower than the Dons in the top-flight, now have a chance for revenge against the favourites.
Aberdeen manager Derek McInnes said: "Whoever we got, it was always going to be tough.
"We know each other inside out and, while we came out on top in the League Cup, that will not have any bearing on this one.
"On the face of it, it's a reasonable draw but that would be the case whoever we got at this stage."
In the other semi, Albion Rovers and Rangers will compete for the right to face Dundee United.
League Two side Rovers and runaway League One leaders Rangers drew 1-1 at Ibrox on Sunday.
They will meet in a replay at Hamilton's New Douglas Park, with a last-four tie against the Terrors - currently fourth in the top-flight - the reward for the winner.
United manager Jackie McNamara said: "We got to the semi-final last year against Celtic and we ran them close, so it would be good to get to the final this year and there is no reason why we can't go on and win it."
The ties will both be played at Ibrox on the weekend of 12th and 13th of April.