The Irishman curled in a beauty in the 31st minute and netted a close range header four minutes later.
Andrew Shinnie increased the lead on 70 minutes when he bundled the ball across the line and a screamer from teenager Philip Roberts rounded off the win two minutes later.
The victory – which included Inverness’ first SPL clean sheet of the season – has drawn them level on points with the visitors.
Inverness suffered an early blow when Ryan Esson injured himself in the warm-up and was replaced by summer signing Antonio Reguero for his first start.
Forward Roberts, who is on loan from Arsenal until January, also made his full debut. The 18-year-old replaced Billy McKay, who scored in Caley Thistle’s midweek cup win at Stenhousemuir, while midfielder Gavin Morrison was preferred to Conor Pepper in the only other change for the hosts.
Dundee United were unchanged from the side who beat Queen of the South midweek in the League Cup.
The visitors started brightly, with Johnny Russell’s cutback finding Jon Daly who fired over.
But it was United keeper Radoslaw Cierzniak at the opposite end who was forced into the first save when he stopped Andrew Shinnie’s low shot.
Reguero made his first save when Willo Flood’s corner found Daly unmarked but his low shot was comfortably saved.
It was a costly miss as Caley Thistle scored a finely crafted goal to take the lead just after the half-hour.
Roberts found Andrew Shinnie who picked out Foran on the edge of the area, and he curled his shot into the top corner beyond the diving Cierzniack.
Four minutes later the 32-year-old added his second when his close-range header found the net from a Roberts cross.
Foran almost turned provider early in the second half when he played in Aaron Doran but the winger blazed his shot over.
United might have pulled one back soon after but Daly’s header was tipped over the bar by Reguero.
Keith Watson was next to try his luck for United but his effort went wide.
Watson was then partly at fault as Andrew Shinnie bundled his way into the area before adding the third goal in the 70th minute from close range.
Roberts put Inverness 4-0 up two minutes later when he blasted a Foran lay-off into top corner from 18 yards.
United failed to create any further clear cut chances to reduce arrears as Inverness comfortably saw out the victory.