The 85-year old woman was found dead in her house on December 19 with a cloth tied around her neck and two bangles missing from her person.
Police said they zeroed in on one Mohammed Sameer Khan (24) in Gandhipuram area near the old woman's house and a team then fanned out across the city to nab him as he was not there.
They said he was nabbed after he jumped from a flyover early this morning on seeing a patrol team and got injured.
He reportedly confessed that he had entered the old woman's house in in inebriated state, raped and strangulated her to keep the crime a secret and also took away the bangles.
After recovering the bangles, police remanded him to custody and he was later lodged in the central jail here.