With Norwich boss Johannes Hoff Thorup making five changes to his starting line-up, including the loss of goalkeeper Angus Gunn to a hamstring injury and dropping captain Shane Duffy to the bench, the home side had an unfamiliar look to it.
But the Canaries came out of the blocks quickly to get their noses in front.
Fisher was set free down the right and his pinpoint cross arrived at the feet of Sargent, who made no mistake from barely six yards to register his eighth goal in eight matches.
Oxford almost struck back immediately but Harris and Ole Romeny both failed to get on the end of an inviting Ciaron Brown cross.
Norwich failed to heed the warning, though.
Vaulks' long throw caused the hosts trouble all evening and his very first missile into the Canaries box led to the equaliser.
Jack Stacey headed the ball against the back of team-mate Anis Ben Slimane and Harris pounced to notch his sixth goal of the season but his first since 26 December.
Another Vaulks throw almost had Oxford in front midway through the first period with home defender Callum Doyle heading just past his own post.
Sargent then had what he thought was his second goal of the night chalked off for offside just before the interval as Norwich finished the first period strongly.
They dominated much of the second period but struggled to create clear-cut chances against a resolute and well-drilled visiting defence.
Ante Crnac saw two efforts saved by Cumming before substitute Oscar Schwartau shot weakly straight at the goalkeeper.
Cumming saved his best for the the final minute as the Championship's joint-top scorer Sainz burst into the 18-yard box but, from a narrow angle, saw the left boot of the U's keeper deny him what would surely have been the winner.
Norwich are three points short of the top six before Saturday's games while for Oxford it is now eight games without a win, but this could prove a precious point as they edge towards safety on their return to the second tier of English football.