Byrne went close to opening the scoring early on but was denied by visiting goalkeeper RyanClarke, while Oxford's Jack Midson missed the target with an ambitious overhead kick.
Despite the loss of Boyd Rankin, who had taken five wickets in the first innings, after Woakes had got rid of visiting skipper James Foster, Clarke took over the role as key strike bowler, knocking back the off stump of both Ryan ten Doeschate and Mark Pettini with fine deliveries.