The umpires called off play at 5:20 pm (0620 GMT) after persistent rain with Australia 103 for two and trailing the tourists by 61 runs after England's first innings ended on the first ball of the day at the Melbourne Cricket Ground.
When play was abandoned for the day, Warner was on 40 with skipper Smith not out 25.
The tourists, with all the momentum after Alastair Cook's record-breaking innings of 244 not out, snared the wickets of Cameron Bancroft and Usman Khawaja to send early jitters through the home side.
England, pressing for their first victory in the already-decided Ashes series, were all out on their overnight total of 491 on the first ball of the day.
Anderson was caught by Bancroft at bat-pad off Pat Cummins for a duck to end the innings. Cummins finished with four for 117.
It meant that Cook achieved the highest score of anyone carrying his bat -- the rare feat of batting throughout the innings -- in Test cricket, bettering New Zealand's Glenn Turner's 223 not out against the West Indies in Kingston in 1972.
Cook set a number of records on the third day yesterday, when he surpassed the highest score by a visiting batsman in a Melbourne Test, bettering the 208 by West Indian great Viv Richards in 1984.
Cook's fifth double-century also catapulted him above West Indian Brian Lara to become the sixth highest run-getter in Test cricket with 11,956.
England have four sessions left in Melbourne to secure their first win of the Ashes series, after going an irretrievable 3-0 down in the first three Tests.
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