Stuart Broad led England to a 169-run victory in the first Test as Australia collapsed either side of lunch on the fourth day at Cardiff's Sophia Gardens on Saturday.
England's successful XI will be joined again by Steven Finn and Adil Rashid as extra bowling options for the second match of five.
Australia, well-placed at 97 for one in Cardiff on Saturday, slumped to 106 for five as four wickets fell for just nine runs in 36 balls.
Chasing a record-breaking 412 for victory, the Ashes-holders were dismissed for 242 after tea.
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Joe Root, named man-of-the-match for his first innings 134 after coming in with England struggling at 43 for three, had the last word in the game by catching Josh Hazlewood in the deep off spinner Moeen Ali.
England captain Alastair Cook has often been criticised for excessive caution in the field but didn't miss a trick in Cardiff and an impressed Bayliss said: "I thought his captaincy was top-notch."
Bayliss, however, added he was expecting Australia to bounce back strongly at Lord's.
"They'll come back hard -- we know that -- and there's still a long way to go in this series.
"To win it, we'll have to play some very good cricket.