Both teams had their chances in a pulsating second half – but the best chance of the game came on 90 minutes, when Arnason met a corner but steered a powerful header inches over the crossbar at New York Stadium.
The Millers, who are now destined to miss out on automatic promotion, dominated the Yorkshire derby but came up against a side who put 10 men behind the ball in a bid to nullify the Football League’s joint top scorers.
After a bright Bradford opening, where Jon Stead fired over a good chance, it was all Rotherham and Alex Revell blazed over a rebound from Ben Pringle’s saved shot, before the striker was just unable to get on the end Kieran Agard’s cross-shot.
The second half followed a similar pattern as Rotherham peppered their visitors’ goal with attacks.
Michael O’Connor hit the upright with a free-kick that evaded everyone, with Nicky Adams seeing his follow-up effort blocked, while Pringle and then James Tavernier were denied by City goalkeeper Jon McLaughlin.
One of their best chances came with 20 minutes remaining when Revell’s knock down found Haris Vuckic in yards of space, but he lazily chipped over.
When Arnason planted a firm header over the bar at the end, Rotherham were denied a deserved seventh successive victory over the Bantams.