Rob Hulse put Leeds ahead from 10 yards after 20 minutes with his 12th goal of the season, but Norwich fought back.
The Canaries were level after 57 minutes when Simon Charlton's pass found Andy Hughes, who shot home.
Norwich were ahead with 15 minutes left when Paul McVeigh fired low past Neil Sullivan, but Lewis produced a moment of inspiration to snatch a point.
Norwich boss Nigel Worthington
"We worked hard and caused Leeds all sorts of problems in the second half.
"It was important we came here in a positive frame of mind.
"Elland Road is a magnificent ground with a wonderful atmosphere but the players got their teeth into the game in good style."
Leeds: Sullivan, Kelly, Butler, Gregan, Crainey, Miller (Bakke 79), Douglas, Derry, Lewis, Hulse, Blake (Healy 69).
Subs Not Used: Bennett, Moore, Kilgallon.
Booked: Derry, Crainey, Gregan.
Goals: Hulse 20, Lewis 90.
Norwich: Green, Fleming, Doherty, Shackell, Drury, McVeigh, Hughes, Robinson, Charlton (Safri 84), Huckerby (Earnshaw 90), McKenzie (Johansson 86).
Subs Not Used: Gallacher, Etuhu.
Booked: Fleming, Doherty.
Goals: Hughes 57, McVeigh 75.
Ref: C Foy (Merseyside).