Barrow ended their Blue Square Bet Premier campaign with a first win in 11 games at Newport's expense.
Andy Cook put the hosts ahead when he converted Jack Mackreth's cross.
Newport fought back and levelled when Ismail Yakubu headed home Andrew Hughes' free-kick.
But it was all Barrow after the break and Richie Baker fired in from 20 yards before Adam Boyes took advantage of Cook's pass and converted from the edge of the area.
VIEW FROM THE DRESSING ROOM
Barrow manager Dave Bayliss told BBC Radio Cumbria:
"To get to 60 points is a good achievement, even though we took so long to get there.
"We were desperate to win for our supporters today. It's been a long time coming and I thought I was having a heart attack at one point and I was desperate to get to 60 points.
"It's horrible going on week in, week out playing OK. Against Kettering last week we had 23 shots and we only scored one goal.
"Today we were clinical in front of goal second half and probably could've had a couple more, but it was important today to win for our supporters."
Newport manager Justin Edinburgh told BBC Radio Wales:
"Disappointed obviously, we're not happy with the result and that sums our season up really.
"We weren't clinical enough in the first half, we had numerous chances to put the game out of sight and Barrow have punished us for that in the second half.
"But that's omething we need to address in the summer and that's why we are where we are; we haven't scored enough goals this season and that came back to haunt us today."