Salisbury made four changes from the team beaten 5-0 in the FA Cup by Lynn a week earlier, and proved a handful to a Lynn defence which again looked frequently stretched.
Lynn made a swift start with a goal after six minutes, albeit thanks to a lack of alertness of referee Paul Carver who had both teams cursing with a poor display.
Richard Skelly gained 20 yards with a free kick taken from the wrong place but Carver failed to see the linesman's flag and, by the time the ball was in the net, his assistant had given up and was sprinting back to catch up with play.
Skelly's kick found Matthews and his crossfield ball saw Lee Hudson shrug off two challenges before slotting the ball wide of new signing James Dungay in the home goal.
Robbie Harbut hacked Jason Pascoe's goal-bound header off the line five minutes later but it was another City new boy who levelled matters after 14 minutes.
Leroy Hales launched a high ball into the area which was allowed to bounce twice before Steve Lewis was caught in no-man's land as Danny Holmes stabbed the ball past him.
Whale pulled a shot wide and Hudson's acrobatic overhead kick hit Dungay as both teams through caution to the wind.
Lewis made a brave save at the feet of Kevin Braybrook but needed lengthy treatment for his actions.
Lynn fell behind after 31 minutes when Colin Hoyle and Tony Spearing leaped for the same ball and it fell kindly for Dave Puckett to head to the unmarked Braybrook who swept it home from five yards.
Lewis was out quickly to snatch the ball from Braybrook soon after but it was Lynn who found the net next, in the third minute of injury time.
Pascoe flicked Matthews' flag kick towards goal and Hoyle applied the neatest of touches to divert it home after missing an easier chance just before.
Steve Williams was denied by the offside flag after 50 minutes for the second time in five days when he converted Hudson's pass but it was a marginal decision.
Chris Male wasted a glorious chance to put City back ahead when he found himself in front of open goal after Lewis had parried Braybook's shot. But the substitute managed somehow to scoop the ball over the bar from 15 yards.
Lewis pulled off another good save to deny Ian Chalk but was then relieved to see a Dave Rickett's shot deflected wide.
Ian Cambridge was brought into the action after 79 minutes and made the crucial breakthrough.
Within a minute he played a cheeky pair of one-twos off defenders near the corner flag and fired a cross goalwards where Wright swept the ball in for his first goal for the club.
Lynn: Lewis, Matthews, Skelly (Ellis, 75), Hoyle, Wright , Spearing, Pascoe,
Williams (Cambridge 79), Roberts, McNamara, Hudson. Subs: (not used) Delicata
Salisbury: Dungay, Parkin (Sergeant 83), Holmes, Baird (Busby 43), Rofe, Braybook, Preston, Whale, Puckett, Chalk, Harbut (Male 45).