Loza was involved again for the second goal as he was brought down inside the area by Ryan Clarke. Lee Barnard stepped up to take the resulting spot kick and sent Clarke the wrong way to double his side's lead.
Clarke was then called into action twice in quick succession at the other end of the field, first denying Timlin's half-volley before tipping the resulting corner over the bar as Kevan Hurst's set piece threatened to go straight in.
A David Hunt corner at the other end caused problems shortly before the half-hour mark as Constable lost his marker and met the cross at the back post, but he volleyed an effort over the bar.
The hosts had another chance to make it 3-0 in the 33rd minute when Loza turned well inside the area, only for Clarke to get down well to make the save.
Oxford were inches away from pulling a goal back right on the stroke of half time as Rigg rose highest in the area to nod an effort goalwards, but Hurst was on hand to clear the danger off the line.