Kieran Gibbs scored at both ends and bagged two assists while fellow defender Micah Richards was also on target for Stuart Pearce’s men, who are unbeaten in three Group matches.
Macedonia’s two other goals came from Muharrem Muharemmi and Agim Ibraimi.
West Ham striker Hines came on at half-time for dead-leg victim Theo Walcott and he hit England’s fourth and sixth goals to seal a memorable debut.
Macedonia had bravely come back from behind on two occasions, first rubbing out a two-goal lead for the hosts, before pulling it back to 3-3 in the second half.
Utility-man Gibbs put England ahead with a 22nd-minute header from Arsenal team-mate Walcott’s cross.
Gibbs turned provider with a corner on the half-hour mark that Manchester City stopper Richards powered home.
The visitors pulled one back three minutes before half-time with Muharrem’s free-kick.
They levelled six minutes after the second-half restart when Ibraimi finished past Scott Loach after Michael Mancienne, on-loan at Wolves from Chelsea, slipped to let him through.
The hosts went back ahead soon after when Gibbs got another assist after a superb left-wing run and cross that Newcastle target-man Carroll sent past Kristijan Naumovski.
But Macedonia equalised again with Gibbs at fault, lashing wildly at a corner and sending it past Loach.
Hines soon restored England’s lead when he raced on to Tom Cleverley’s pass and slotted the ball past Naumovski.
Carroll made it 5-3 with three minutes remaining after four team-mates missed chances to convert during a goalmouth scramble and Hines added a sixth with a close-range volley in injury-time.
England now have seven points from three matches after winning their opening match in Macedonia and drawing in Greece.
The Republic of Ireland, meanwhile, slumped to a draw at home to Georgia.
Alan Judge put the hosts ahead just before the half-hour mark but Giorgi Ivanishvili injured with one minute remaining to give the visitors a surprise point.