Skirmishes broke out near the National Arena with rival fans throwing fireworks and smoke bombs at each other while Hungarian "ultras" destroyed the buses they were in because their national flag was wrongly printed on the information guide they received.
There was an electric atmosphere at the stadium, with both teams' fans creating a deafening roar and letting off dozens of firecrackers and flares shortly before kickoff.
Tempers boiled over throughout the encounter, with fans warned by the stadium announcer about their behaviour on several occasions and riot police spraying tear gas.
Romanian Football Federation president Razvan Burleanu criticised riot police action during clashes with fans, describing it as "unjustified violence".
Hungarian supporters set several seats on fire when Adam Szalai had a goal disallowed for offside six minutes before the break.
Police spokeswoman Irina Dragan said five of the arrested Romanians have been banned from soccer stadiums for one year, adding that nearly 12000 police and security forces were deployed in and around the stadium.