Baker stabbed the Saints into the lead in the 12th-minute after a superb ball into the box from Craig Jones and went close to adding another soon afterwards, when his header from a Chris Marriott flag-kick hit the angle of post and bar.
But TNS generally failed to trouble Wingmakers' keeper Kristian Rogers, with Alex Darlington rounding off a good move by placing his shot straight at the stopper.
Ashley Williams was inches wide of an equaliser in first-half stoppage time with a 22-yard effort and, when Darlington surrendered the ball in midfield just after the break, only an excellent save from Paul Harrison kept out a shot from Paul McManus after a one-two with Williams.
Jones was just wide from 25-yards after an excellent run and Chris Sharp spurned a gilt-edged opportunity on 65 minutes from a Danny Holmes throw-in.
The visitors appealed for a penalty when Nick Rushton's shot cannoned off a defender's arm and there was general relief when Jones settled the game in the 76th-minute with a superb solo effort, cutting inside two defenders before unleashing a shot into the far corner.
Danny Holmes was just wide with a long range effort, but Carl Owen almost had the last word for the Airmen with a header that looped just wide of the far post.
Photo: Chris Sharp celebrates with goal scorer Phil Baker.