The Uppsala District Court said one of the men was given a sentence of 27 months for rape and assistance to rape. The others were given respectively one year - which was halved because he was a minor at the time of the crime - and six months.
Judge Nils Palbrandt said on Tuesday the woman who was under influence of narcotics was not able to give her consent to the sexual act, as was claimed by the men.
The teenager and two men in their 20s were arrested in January in Uppsala, north of Stockholm, after police received tips about the streaming and the rape.
The court ruled that the crime was "aggravated as the film clip received widespread attention in Sweden and abroad, and caused great harm to the injured party."
The trio - who denied the charges - were arrested after police were alerted to the January 22 crime that was filmed and live-streamed for a private group on Facebook.
In addition to prison terms, the court ordered the trio to pay damages totalling 330,000 kronor ($A49,678) to the unnamed woman.
During the course of the trial, prosecutors said they received a complete film clip from Facebook showing the incident, arguing it strengthened their case.
Testimony from several witnesses who saw the live stream was also part of the case.
At the closing of the trial, the prosecutors also dropped an initial request that the two younger men should be deported to Afghanistan, if convicted.
Most of the trial was held behind closed doors.
The court ordered that the identity of the victim, a woman in her 30s, remained sealed.
