Chris Rogers was 50 not out and Mitchell Starc one not out, with Anderson having taken five for 23 in 11 overs when rain halted proceedings for 20 minutes at 2:55pm local time (1355 GMT).
It was an impressive turnaround for Anderson, England's all-time leading Test wicket-taker, who went wicketless during Australia's 405-run second Test win at Lord's with match figures of none for 137.
Australia captain Michael Clarke won the toss and batted despite the overcast conditions and green-tinged pitch which promised to offer more sideways movement than was on offer at Lord's.
The tourists were indebted to Rogers, the 37-year-old left-handed opener, who scored his ninth fifty in 11 Test innings on Wednesday.
Rogers, who plans to retire after the end of the Ashes, was given the all-clear to play at Edgbaston after suffering a dizzy spell at Lord's caused as a result of being hit on the head by an Anderson bouncer during the course of his Test-best 173 in the first innings.
The five-match series is level at 1-1 after England won the first Test in Cardiff by 169 runs.