Mike Samwell, 35, was fatally injured as he tried to prevent thieves from stealing his car from outside his home in Chorlton, Manchester on Sunday.
A 20-year-old man from south Manchester has now been arrested on suspicion of murder and is in custody.
A 21-year-old man arrested on Monday has since been released on bail.
Mr Samwell was asleep with his wife Jessica in their Cranbourne Road home when intruders struck in the early hours.
Police believe he was run over by his car, a black Audi S3, which was taken and later found damaged about three miles away from the house.
Mr Samwell's family paid tribute to him and described him as a "special, kind and exceptionally talented man".
Greater Manchester Police are continuing to investigate and have appealed for anyone with any information to get in touch.
A second man has been arrested in connection with the death of an ex-Royal Navy officer thought to have been run over by his own car.