Carpenter was sentenced to six months in prison and disqualified from driving for 18 months.
Sebury received an 18-month community order and was disqualified from driving for 12 months. He also has to complete 150 hours of community work.
"This incident was a classic case of road rage where two motorists have driven dangerously, at high speeds, undertaking, tailgating and flashing their lights," said PC Kathryn Matthews of the South Wales Police Roads Policing Unit.
"It is sheer luck that nobody was killed or seriously injured and the dashcam footage of the incident sends out a clear message about the consequences of driving in such an irresponsible manner."