At the close Strauss had reached 161 not out, his 18th test century and third against Australia, and also passed 5,000 runs in test cricket.
But England failed to take advantage of an opening stand of 196 between Strauss and Alastair Cook (95) and their score of 364 for six was no more than adequate on a bland Lord's pitch.
Strauss and Cook sped to 126 for no wicket at lunch against some wayward bowling, particularly from the Australian spearhead Mitchell Johnson who conceded 53 from eight wayward overs.
Australia regrouped, despite the loss of off-spinner Nathan Hauritz with a dislocated finger in his bowling hand, while the England middle-order gave their wickets away.
Strauss, batting at the headquarters of his county team Middlesex, took full toll of some disjointed Australian bowling in the opening session as England raced to 126 for no wicket at lunch.
He lost Cook lbw to a rare straight ball from Johnson after a splendid partnership which left Australia in seeming disarray after having much the better of the drawn first test in Cardiff.
DISLOCATED FINGER
Strauss was dropped on 52 when he launched a ferocious drive at Hauritz, who got his right hand to the ball and dislocated the middle finger. He left the field immediately for lengthy treatment.
Ravi Bopara drove the ball sweetly through the covers with an extravagant flourish but failed to take advantage of the situation and the conditions.
He had scored 18 from 19 balls when he played around a Hilfenhaus delivery for the second time in as many innings and was adjudged lbw.
Kevin Pietersen played a bizarre cameo for 32 which seemed entirely at odds with his side's requirements.
He scampered his customary risky singles at the start of his innings, stole the strike from Strauss who was moving serenely to his hundred and came dangerously close to handling a ball that looked like it was running on to his stumps.
An attempted hook off the next ball fell safely on the leg-side.
He appeared to settle down after tea, driving two majestic fours before Peter Siddle ran a delivery away from the bat and Pietersen nibbled a catch to wicketkeeper Brad Haddin.
Paul Collingwood (16) chipped a simple catch to deep mid-on off Michael Clarke and Matt Prior (8) was bowled by a Johnson delivery through the gap between bat and pad.
Andrew Flintoff entered to loud applause for his last test at Lord's but departed after only 16 minutes for four.
England predictably chose four pace bowlers, omitting spinner Monty Panesar. Graham Onions won the final place ahead of Durham county team mate Steve Harmison.
Australia kept faith with their first test XI.
