The International Development Secretary lost support in the third ballot of Conservative MPs and came last, with just 27 votes. Boris Johnson stretched his lead further, picking up 17 new votes for a total of 146, nearly half of the parliamentary Conservative Party.
Mr Stewart, who had suggested there were "dark arts" at work in the ballot with reports that Mr Johnson was 'loaning' votes to other candidates, has already opened talks with Michael Gove about a possible joint ticket.
The Environment Secretary picked up 10 new votes, putting him on 51, just three behind Foreign Secretary Jeremy Hunt, who gained eight votes for a total of 54. It sets up an intense fight between the two cabinet ministers for second place and the right to face the favourite, Mr Johnson.
Home Secretary Sajid Javid gained 5 votes to finish in fourth, on 38, but is the most likely to go out next when the final two ballots take place on Thursday.