"To win by as big a margin as that is testament to the 11 guys who played for England," captain Alastair Cook said. "There were some times when we were under pressure, like at 30-3 on the first morning."
Australia badly needs to improve ahead of the third test at Old Trafford on August 1, especially in its batting department.
"I'm still confident we can win this series," Australia captain Michael Clarke said. "I know the crowd laughed when I said that and rightly so with the position we are in right now, but all of our top order have made a 50 and we need someone who can go on and make a big hundred, as England have done. We need to perform better to win this third test but we have time to prepare."
The tourists faced an unenviable task from the outset given that West Indies' 344-1 in 1984 was the highest score to win a Lord's test.
England delayed its declaration Sunday morning so Root could reach his maiden double century, but he faced just four balls in 15 minutes and was caught at third man off Ryan Harris trying an audacious ramp shot over the wicketkeeper's head.
Root batted for almost eight hours, striking 18 fours and two sixes, to cement his position as Cook's opening partner after Nick Compton's omission before the series began.
Australia made the worst possible start in its unlikely attempt to bat out the final two days. Shane Watson (20), Chris Rogers (6) and Phil Hughes (1) all departed in the 22 overs before lunch.
James Anderson trapped Watson lbw, with a ball that came back into him down the Lord's slope. It was the 10th occasion Watson had been lbw in 19 test innings against England.
Opener Rogers was bamboozled by Swann's trickery and played no stroke at a ball he thought was going to spin away but went straight on to bowl him. Hughes was lbw by Swann.
Clarke, who should have been stumped by wicketkeeper Matt Prior when on 2, fought back and put on 98 with Usman Khawaja. But Clarke eventually clipped an innocuous ball from Root to leg slip for 51.
Khawaja batted maturely and looked as though he was going to survive the afternoon session until he drove Root to Anderson at gully. That was after he came through an England review on the same score after the ball hit a footmark and was caught by Jonathan Trott at slip.
Steve Smith fell to the last ball before tea, caught behind off Tim Bresnan, though Smith failed in his bid to review his dismissal, with the third umpire Tony Hill upholding the onfield umpire's decision, apparently due to a slight mark on hotspot.
That was 136-6 at tea, soon to become 162-8 after another controversial failed review by Ashton Agar, who did not feel he edged Bresnan to Prior. Brad Haddin was lbw to Swann.
Last-wicket pair James Pattinson (35) and Ryan Harris (16) threatened to take the match into a final day with a stand of 43 in 62 minutes, but Swann trapped Pattinson lbw with three balls remaining in the day.
- AP