The result is big blow for United’s hopes of clinching a European spot after St Johnstone’s moved a point ahead of them with a 0-0 draw against Celtic on Friday evening.
Inverness created an early chance when Ryan Christie collected a short corner and drove to the goal-line before crossing for Edward Ofere to head just over the target.
The home side had another opportunity after Ross Draper played a reverse pass inside to Graeme Shinnie, but the defender dragged his shot wide from close range.
And Inverness squandered a better chance when United defender John Souttar fluffed a clearance to Aaron Dorans to fire wide from 10 yards with the goal at his mercy.
United threatened two minutes before the interval when John Rankin tested Ryan Esson with a powerful drive but the Caley goalkeeper saved well.
Esson was again forced into action three minutes into the second half when he made a terrific block to thwart Nadir Ciftci after the United striker produced a neat piece of skill.
The breakthrough came on 55 minutes though as Gary Warren rose to meet a corner at the back post and Meekings pounced from close-range despite the best efforts of Robbie Muirhead who used his hand to try and block, but the ball was already over the line.
Marley Watkins almost doubled the advantage on 61 minutes when the substitute raced down the left flank and placed a shot narrowly wide of the far post, shortly before Meekings sent a back-heel straight at goalkeeper Rado Cierzniak.
United then squandered a wonderful chance to level when Ciftci drifted into space inside the penalty area but shanked the ball well over the target.
But with 10 minutes remaining United fell further behind when James Vincent had his net-bound shot blocked by team-mate Meeking, but the ball broke to Ross to smash home.
And Caley completed the victory on 83 minutes when Warren powered his way through a bunch of players to connect with a cross from the left flank to head into the net.