Bogus officials held a cushion over the face of an 85-year-old woman in her Bolton home as they struggled to take her handbag from her.
Two men went into her house in Levens Drive on Wednesday lunchtime, claiming they were checking her water supply.
One picked up a shopping bag so she grabbed her handbag and keys which one man tried to wrestle from her. She screamed and he tried to smother her.
Police believe the men also stole cash from another woman, 91, shortly before.
A man knocked on her door in Barchester Avenue between 1230 and 1300 GMT and told her she had a problem with her water supply.
He distracted her while another man stole the money.
One of the men was described as in his 20s, while the other was in his late 30s to early 40s. Both were about 5ft 4in (1.6m) tall.
Pc Lee Gridley, of Greater Manchester Police, said: "This pair carried out a despicable attack on a vulnerable elderly woman.
"They are clearly desperate and I believe they will stop at nothing to take money from vulnerable people.
"I now want to hear from anyone who saw these men acting suspiciously around that time or from anyone else who may have been targeted by these chancers."