Boris Johnson races ahead in latest Tory leadership vote
But there was another overwhelming victory for Mr Johnson, who secured 126 votes - 80 ahead of his nearest rival Jeremy Hunt on 46.
Michael Gove was in third place on 41 votes, while Rory Stewart was on 37.
Candidates needed 33 votes to remain in the race - the exact number picked up by Mr Javid.
Mr Raab's hopes of replacing Theresa May in Downing Street were dashed after he secured just 30 votes.
The remaining candidates were taking part in a BBC debate before further votes on Wednesday and Thursday will whittle the field down to a final two.
With Mr Johnson appearing certain of a place in the final two, the contest has become a battle for the right to a spot alongside him in the ballot of 160,000 Tory members who will choose the next party leader and prime minister.
International Development Secretary Mr Stewart's result came after he secured just 19 votes in the first round.
A campaign source said the extra 18 votes showed "his momentum is continuing to build", and "he can now go all the way to the final two, giving the clear choice that members deserve".
But it would appear unlikely that many supporters of the hard-Brexiteer Mr Raab will switch to Mr Stewart, so for his campaign to go further he will have to win over MPs from rival campaigns.
Mr Javid picked up 10 votes from his first-round tally to scrape through to the next ballot on Wednesday.
Environment Secretary Mr Gove picked up just four extra votes, but said he was "very pleased to have made it through and closed the gap to second".
In an apparent warning to Tories about the prospect of Mr Stewart, who voted Remain in 2016, making it through onto the final ballot paper, Mr Gove stressed: "The final two should be Brexiteers who are able to take on (Jeremy) Corbyn, unite the party and deliver Brexit."
Mark Francois, vice-chairman of the Brexit-backing European Research Group of Tories said he hoped Mr Raab would be given a seat in Cabinet.
"It was great to see Boris going up again - that's obviously encouraging," he said.
"In a sense it's a shame to lose Dominic Raab because he is an extremely capable politician.
"I hope whoever wins - and I hope it's Boris - will find a good place for Dom in his Cabinet."