England set 371 to win second Ashes Test after Australia out for 279
England took eight wickets for 149 to leave themselves a victory target of 371 to square the series.
If achieved, it would be the highest successful fourth innings run chase ever in a Lord's test, beating the 342 West Indies hunted down to beat England in 1984.
Australia began the day in command on 130-2 having bowled England out on Friday for 325 for a lead of nearly 100.
Usman Khawaja and Steve Smith looked set as they moved the lead towards 300 in the morning session but they were out for 77 and 34 respectively, both playing rash shots.
Travis Head was out for seven fending off a well-directed short ball by Broad to leave Australia on 222-5 at lunch.
Australia's scoring rate dried up to a trickle in the afternoon as England's 'Bazball' tactics turned into snooze ball as they fired down bouncer after bouncer to a leg side field.
One by one, Australia's batsmen lost patience with wickets falling regularly, Broad ending with four and Ollie Robinson taking two for seven runs from a nine-over spell.
Australia's innings ended in farcical fashion with injured spinner Nathan Lyon coming out to bat despite being unable to run after injuring his calf on Thursday.
A courageous Lyon managed to hop one single after Mitchell Starc's attempted six was miraculously flicked back from the boundary rope by substitute fielder Rehan Ahmed.
With every England fielder on the boundary, knowing Australia's only hope of adding runs was fours or sixes, Starc smashed one six off Josh Tongue and a one-legged Lyon got a huge cheer from the Australian fans as he swatted a boundary.
Lyon was eventually out as he top-edged Broad to Ben Stokes at square leg to end a short but remarkable cameo.
In just the third over of the run chase though, England were 9-1 having lost Zak Crawley to a fine edge down the leg-side off of the bowling of Starc, taken well by wicketkeeper Alex Carey.
