Josh O'Keefe netted an early opener for the Imps but Steve MacLean pulled Oxford level in the 40th minute following goalkeeper Trevor Carson's fumble.
But two own goals in the space of four minutes gave the home side victory as Harry Worley hooked a 63rd-minute volley into his own net, only to be followed up by team-mate Anthony Tonkin repeating the mistake shortly afterwards.
Tilson said: "It was a big win for us and we really needed it because they are a good side. They passed it well, which makes the result even better.
"Josh O'Keefe did well for the first goal, you can't really explain what happened for their equaliser. But we dug in, and some keen spirit and a little bit of togetherness got us the result.
"We`ve got a long way to go, I have to concentrate on this year and get the points on the board, as much as I want to start thinking about next season."