Councillor Chris Petersen agreed, saying council had put aside $65,000 "in total" to help with the road and entrance.
He said it was likely Masterton Motorplex "will come back to us yet again" for money and "we are likely to support them in the future".
Referring to work done by volunteers on forming a gravel road from Manaia Road to the drag strip, Councillor Simon O'Donoghue said motorplex chairman Bob Wilton had already succeeded in "halving the cost".
He said the $28,692 now being sought would give the drag racing fraternity "an operational track".
Councillor Pip Hannon said she was divided on the issue.
"Bob Wilton has done much and I feel mean for saying this but giving the money means someone else misses out, some other sporting code," she said.
Councillor David Holmes said he supported giving them the full amount sought.
"I put my hand up and say yes.
"I back anyone, such as Bob Wilton, who goes out and does it," he said.
Deputy mayor Graham McClymont suggested a compromise by giving Masterton Motorplex half the amount asked for, being $14,500 but this was eventually voted down on a show of hands 3-7 and the motion to grant the full amount was carried.