Biros was pronounced dead about 10 minutes after the injection was administered, the Associated Press news agency reports. On average, death took seven minutes under the previous method in Ohio.
The total process of Biros' execution lasted for about 43 minutes, AP said, adding that the execution team took about 30 minutes to find a suitable vein for the insertion of the needle.
The change of approach follows a failed attempt to execute a prisoner in Ohio in September, when officials struggled for two hours to try to find a suitable vein into which to inject the drugs.
All executions were put on hold while another method was sought.
LETHAL INJECTION
Used in all 36 death penalty states in the US
Three-in-one injection contains an anaesthetic, muscle paralyser and a heart stopper
The new injection contains a large dose of anaesthetic alone
Lethal injection choice on trial
The Ohio Department of Rehabilitation and Correction had estimated that it would take 15 to 30 minutes for prisoners to die using the new method, but also that it would be less painful.
Officials rejected suggestions that the technique was experimental, noting its widespread use as an anaesthetic.
"It's not an experiment drug, it's used in existing protocol and it's used in hospitals all across this nation and in the world," Terry Collins said.
Other states which have the death penalty were reported to be watching closely but some - including Florida, Kentucky, Texas and Virginia - have said they intend to keep the triple-drug method.
Of the 36 death penalty states which have lethal injection as a means of execution, all but Ohio favour the three-drug method.
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