Caton tapped in the opener from close range after Southport keeper Max Crocombe failed to handle a corner.
The on-loan Shrewsbury winger collected Jack Muldoon's pass and shot low past Crocombe to double the lead.
Louis Almond pulled one back for the visitors with a strike from the edge of the area, but Robbie McDaid fired in to seal the win late on.
Lincoln City manager Chris Moyses told BBC Radio Lincolnshire:
Media playback is not supported on this device
"We were very good at times. They had a 15-minute spell where they came into it and got a goal but we went again and some of our football was top-drawer.
"You have to back yourself, trust yourself and believe and that's what this group keep doing. They believe in themselves. They're a very positive group.
"James Caton is great with the ball, he causes defenders all sorts of problems and it's given us another dimension. We're a lot more fluid when we break. We've got plan B and plan C and that's good."
Two goals from James Caton helped Lincoln City earn a comfortable victory over Southport in the National League.