Kara Louisa Robinson, of Manor Estate, appeared at Nuneaton Magistrates Court for sentencing on Tuesday 11 February.
She was found guilty in her absence at a hearing in January of failing to notify the council of a change in her circumstances.
Magistrates heard the council launched an investigation into Miss Robinson's circumstances after receiving an anonymous tip-off.
Officers from the council's benefit investigation team discovered the 34-year-old's partner had moved into her home, but she had failed to inform the council and had carried on claiming housing benefit.
She had also failed to tell the council she had changed jobs.
The court heard Miss Robinson fraudulently claimed a total of £5,902.07 in housing benefit from 1 May 2012 to 27 October 2013.
After considering a report from a probation officer, magistrates sentenced Miss Robinson to a community order with nine months supervision. She was also ordered to pay a £60 victim surcharge.
The council can recover the overpaid housing benefit from Miss Robinson.
Speaking after the hearing, Cllr Leigh Hunt, Rugby Borough Council portfolio holder for sustainable inclusive communities, said: "We're determined to crackdown on benefit fraud, and have no hesitation in taking action through the courts when necessary.
"However, while we're committed to catching those who cheat the system, we're also here to help.
"I would urge anyone who has concerns about their benefit claim, or who is uncertain about how their circumstances affect their claim, to contact the council's benefits team on (01788) 533433."
Residents who wish to report suspected cases of benefit fraud can call the council in the strictest confidence on (01788) 533460 or email
benefits.unit@rugby.gov.uk