Paul Gallagher had a penalty saved by Leeds goalkeeper Neil Sullivan, who late on pushed substitute Hannes Sigurdsson's shot onto the woodwork.
And with 22 minutes remaining Jonathan's Douglas cross from the right somehow evaded the Stoke defence, leaving Lewis to score from five yards.
Stoke's luck was summed up in stoppage time when Michael Duberry's close-range effort come back off the bar.
Leeds manager Kevin Blackwell:
"To get promoted you need Lady Luck to smile on you, and the physical desire for a fight if you need one, then you can win it by good football.
"It's a whole raft of things and the players are showing the work ethic and the desire to put their body on the line when they need to.
"But we've got skill as well with the likes of Eddie Lewis, David Healy and Robbie Blake, who can open people up."
Stoke: Simonsen, Halls (Buxton 75), Duberry, Hoefkens, Broomes (Sigurdsson 82), Gallagher, Russell, Brammer, Chadwick, Bangoura, Sidibe.
Subs Not Used: de Goey, Sweeney, Henry.
Booked: Chadwick, Gallagher.
Leeds: Sullivan, Kelly, Butler, Kilgallon, Harding, Lewis, Douglas, Derry, Cresswell, Healy (Miller 66), Blake (Hulse 82).
Subs Not Used: Pugh, Richardson, Bennett.
Goals: Lewis 69.
Ref: M Halsey (Lancashire).