Lee claimed 5-49 off nine overs at Lord's on Saturday to restrict the hosts to 220, while Australian opener Tim Paine scored his maiden international half-century in a seven-wicket win.
Paine hit 51 off 62 balls as the Australians reached 3-221 with 6.2 overs remaining.
Refreshed from his post-Ashes break, captain Ricky Ponting contributed 48, while deputy Michael Clarke was unbeaten on 62.
Nathan Hauritz took a valuable 2-23 off his 10 overs for the tourists as England's batting woes continued, but it was Lee who proved the destroyer.
Having missed the entire Ashes campaign, the paceman bowled with lightning speed and produced a devastating spell in which England lost their last five wickets for 20 runs in 22 balls.
Not for the first time in the series it fell to Andrew Strauss to hold his side's innings together, but again the England skipper failed to capitalise.
He brought up his 50 with his eighth four while sharing a 67-run partnership with Ravi Bopara (26), but it was another 11 overs before England found the boundary again.
Bopara fell victim lbw to Hauritz and the off-spinner struck again when Strauss skied a top edge to Nathan Bracken at short third man to be out for 63, the same score he reached in the previous match.
Lee had already dismissed England opener Joe Denly (11), caught at slip by Cameron White.
When he returned to the attack, he bowled Matthew Prior (29) with an in-swinging yorker on the first ball of his new spell, which only lasted one maiden over.
Another Lee yorker accounted for Luke Wright (12) and the 32-year-old struck again two deliveries later with a ball that uprooted Stuart Broad's leg stump, dismissing the dangerous Ashes star for two.
Lee grabbed his fifth scalp with yet another yorker that demolished Adil Rashid's stumps, dismissing the batsman for four.
Playing just his fifth one-day international, Paine came to the crease keen to build on the starts he had made in the previous two matches, where he scored 26 and 29.
In the side for injured first-choice wicketkeeper Brad Haddin, Paine hit five fours on the way to his score, but fell shortly after bringing up his milestone, caught behind by Prior off leg-spinner Rashid.
Ponting faced 60 balls and hit five fours but was out to a sharp catch by Bopara at short cover off the bowling of Tim Bresnan.
Clarke brought up his 50 with a well-placed four just wide of cover and Callum Ferguson hit the winning run - a scampered single - to remain not out alongside him on 23.
