Rovers are now unbeaten after three league games this term - they also accounted for Championship side Crystal Palace in the Carling Cup - but their run goes all the way back to April Fool's Day.
That is 14 matches without defeat for head coach Paul Trollope, who proudly watched his team stage a superb defensive show under pressure at Boundary Park.
Oldham created chances but the visiting back four hardly put a foot wrong as Steve Elliott gave a man-of-the-match display.
Oldham started well and had the majority of possession, but Rovers showed their own quality up front by making chances which Rickie Lambert and Richard Walker helped over the crossbar.
They almost broke through on 24 minutes when David Pipe delivered a pinpoint cross from the right and Lambert sent his close-range header crashing into the woodwork.
Oldham full-back Neal Eardley, who made his full Wales debut at the age of 18 on Wednesday night, picked out Chris Taylor at the other end but the winger headed off target.
And Rovers gained their precious advantage seven minutes before half-time as Walker crossed to Jacobson and the recent signing from Cardiff rose to score with a header from six yards.
Walker missed a difficult chance early in the second half and Oldham gradually got on top as they searched in vain for an equaliser.
Michael Ricketts headed wide midway through the half and Taylor unleashed a 25-yard thunderbolt which skimmed the bar.
The final opportunity fell to substitute Deane Smalley on 83 minutes, but he somehow missed the target from inside the six-yard box after a cross by Craig Davies.