Alan Marlow targeted his victim as she walked down the street at the back of the Library of Birmingham on the afternoon of Friday 28 February.
The 43-year-old, of no fixed address, pushed the woman to the ground at around 3:45pm and assaulted her, before snatching her mobile phone.
A passer-by heard her screams and gave chase but was threatened by Marlow, who told him he had a knife and to back away.
Undeterred, the man continued to chase him and was joined by a second member of the public who helped grab and restrain him.
Despite a violent struggle, during which Marlow assaulted one of the men, they were able to hold on to him until police arrived.
He was arrested, charged and later admitted robbery and assault.
Marlow was sentenced to eight years in prison for robbery and 12 months for assault, to run concurrently, at Birmingham Crown Court on Monday 14 April.
DC Jamie Simon, from Birmingham CID, said: “Thereâ€™s a good chance heâ€™d have got away had it not been for those two members of the public who stepped in when they witnessed the robbery.
“One of them got a bloody nose and a cut lip for his troubles, but hopefully heâ€™ll be pleased his efforts paid off in the end and to see that justice has now been done.
“It was a great result – we were able to arrest Marlow there and then, so were able to recover the stolen phone and get it back to the victim as soon as possible.”