Motherwell made a perfect start to such a crucial game when they opened the scoring after only eight minutes.
Steven Hammell bent a cross from the right into the Inverness penalty area where it was met by the head of Porter.
His effort left Ryan Esson helpless from eight yards out for Well's first goal in over four games.
The home side were dominant and Esson had to look lively to save from both Porter and Maros Klimpl.
Well were also denied what looked a stonewall penalty when Ross Tokely appeared to have barged Stephen Hughes in the back but not nothing was given.
Then with six minutes to the break, the home side added the second goal they deserved and it was Porter once again, this time heading home a Paul Quinn cross.
With two minutes to the interval, Inverness scored an unlikely goal with their first real attack when a Dougie Imrie corner was headed into the air by Well's Hughes and Tokely was on hand to head into the empty net.
The opening stages of the second half saw a flurry of activity with chances falling for both sides, with Garry Wood shooting wide for the visitors, while at the other end David Clarkson headed a Hughes cross just over.
Nerves seemed to take over as neither side could find any fluency until Motherwell scored a third goal with 12 minutes left.
A Hammell free-kick was bent into the six-yard box and Porter headed in his own and his side's third from close range.
Motherwell looked to be coasting to a comfortable victory but Inverness kept plugging away and pulled another goal back in stoppage time.
The referee judged that Stephen Craigan had climbed all over Andy Barrowman for what looked a soft penalty award.
Adam Rooney saw his initial effort saved by Graeme Smith, but the ball fell kindly for the striker to score from close range.
However, it was all a little too late for the visitors as Motherwell clung on for victory.