The 29-year-old split from husband Jordan Bratman earlier this year and was recently spotted enjoying a night out at the Abbey in West Hollywood with Rutler.
An onlooker said: 'Christina was in a great mood and seemed very into Matt.'
The US singer spent Thanksgiving with her friends in LA while her son Max, two, spent the holiday with his father.
A source said to PEOPLE: 'This is the first Thanksgiving she was without Max. It was really hard for her and she was feeling sad, so she decided to go to the East Coast with Matt and a group of friends.'
While in Rhode Island, they took a trip to Rutler's family home where Aguilera met his mum Kathleen.
The source added: 'Since his family lives so close, they decided to drop in for a few hours.'