Sheehan found himself unmarked in the box and buried a Ben White cross into the bottom corner on 57 minutes before Hayes confirmed the win in the fourth minute of added time, slotting in after a pass from substitute Frank Nouble.
The Exiles had Joe Day to thank for keeping them in it at times, who denied Connor Smith’s quick free-kick by scrambling across his line and from the resulting corner the goalkeeper beat away an Omar Sowunmi header.
Day then stopped Francois Zoko from hitting the equaliser after Sheehan had opened the scoring, firstly making himself big to block an effort inside the six-yard box and then brilliantly diving across goal to claw a header out.
The visitors also went close through Padraig Amond whose header forced Jonny Maddison to tip it over but it didn’t matter in the end as they ran out comfortable winners.
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.