The second goal, against the run of play, happened when a ball played across Hayward's goal found a lone Redsox player among a posse of City defenders who shinned home.
The second half was played at a little less pace when the hosts gained possession and left City with little opportunities.
Apart from a smart chip by substitute Jordan Hodgkinson, the visitors were left ruing their decision making in and around their opposition's penalty area.
City could be accused of not crossing the ball into dangerous areas to test the Redsox defenders.
After another late speculative free kick from their own half, Redsox netted when Hayward (Jnr) again slipped.
Combined with a stiff breeze, the ball floated just beyond his reach.
Coach Hayward will have to address his side's inability to deal with the long, direct ball as again City were undone.
It is an issue that has been discussed and one that will now have to be rectified.
While Redsox may well consider the score a comprehensive victory, they well know it was indeed a little flattering as they rode their own amount of good fortune in the first half and could well have been the side behind.
But such is the nature of the game that those who don't put away their chances will be punished.
For City, it is now about converting the chances.
Thursday was an opportunity for City to close the gap on the competition leaders and now they have to regroup after today's bye, hopefully getting players back from injury, and look to restart.
The onus is now on the coaching staff to lift the group and forge onwards towards some more positive outcomes.
