Snaresbrook Crown Court heard how Siddique got off the number 55 bus while Ahmad began chatting to the woman when she realised she had missed her stop.
Ahmad persuaded her to get off at the next stop and said he would call her a taxi. He then phoned Siddique, a student at the London College of Business Management and Information Technology, to summon him to the scene.
The two men lured their victim down a secluded alleyway off Leabridge Road in Leyton, east London, and took turns to rape her in the early hours of June 4 last year.
During their trial Ahmad and Siddique insisted their victim had encouraged them, but the jury found both defendants guilty of rape and attempted rape.
Judge Tudor Owen said he believed the pair should be kicked out of Britain once they have served their jail terms, adding: ?The sooner you are deported from this country, the better.?
In an impact statement the victim said the attack will ?stay with her for the rest of her life?.
But she is determined to ensure her ordeal does not dictate her future.
Sentencing, Judge Owen told the two rapists: ?What you did was despicable. Your story was simply ludicrous.
?You claimed she instigated the whole thing, that it was she who wanted to engage in sexual activity with you.
?Unsurprisingly, the jury rejected your account.
?Women travelling alone at night are entitled not to be accosted in the way you two did.
?She had a lot to drink but that does not mean she should have been treated in the way she was.
?She was an easy target because she was so drunk.
?She is now frightened of travelling alone at night, this has damaged her life.?
Jailing Ahmad for 10 years, and Siddique for eight-and-a-half years, Judge Owen added: ?If it is necessary I will recommend most strongly that you are deported at the conclusion of your sentence.?
Ahmad, of Spruce Hills Road, Walthamstow, east London, and Siddique, of Gainsford Road, also in Walthamstow, denied rape and attempted rape.
Judge Owen commended investigating officer Detective Constable Jonathan Concanon for his part in bringing the rapists to justice.
The detective, of the Metropolitan Police?s specialist sex crime unit Sapphire, said: ?Ahmad and Siddique demonstrated they are predatory offenders. They lulled the victim into a false sense of security before attacking her.
?The victim showed immense bravery in coming forward and reporting this horrendous attack. I hope knowing her attackers are now behind bars will go some way towards allowing her to come to terms with what happened and to go on to have as fulfilling a future as possible.?