Brisbane: Australia set England a daunting 561 to win but Harris and Johnson struck once each to reduce the hosts to 24/2 at stumps on Day 3 in opening Ashes Test at the Gabba on Saturday.
Australia declared their second innings at 401 for seven, setting England 561 runs to win.
Skipper Michael Clarke declared with about an hour left on the third day giving his bowlers just over two days to attempt to bowl out England and take a 1-0 lead in the Ashes series.
England will have to create Ashes history to win the Gabba Test with their previous highest winning fourth innings score at 332 for seven in Melbourne in 1928.
The world record for the highest successful run chase is the West Indies' 418 for seven against Australia in Antigua in 2003, while the highest winning chase at the Gabba is Australia's 236 for seven against the West Indies in 1951.
David Warner (124) and Clarke (113) scored centuries, while wicketkeeper Brad Haddin scored half-centuries in both innings with 53 off 55 balls in the second innings.
Chris Tremlett finished the best of the England bowlers with three for 69, while spinner Graeme Swann took two for 135 and Stuart Broad two for 55.