Ross also scored in added time as the lead changed back and forth in a tie which will have to go to a replay.
Billy McKay had put the visitors ahead at the Global Energy Stadium on the half hour only for Rocco Quinn to equalise four minutes into the second half.
Foran put Caley back in front with 16 minutes to go back County were level again when Iain Vigurs netted with four minutes left on the clock.
Richard Brittain put the home side ahead for the first time in the second minute of added time but Foran ensured the spoils were shared.
The visitors started well and a deep cross from David Raven caused concern in the County defence but the ball was eventually cleared.
Caley Thistle forced the first corner of the match in the eighth minute when Mark Brown failed to keep a Scott Boyd knockback from going over the byline, but it came to nothing as Graeme Shinnie's effort was booted clear.
In County's first real attack Marc Fitzpatrick's cross from the left was knocked down in the box by Gary Glen but there none of his team-mates reacted and the moved fizzled out.
In another sweeping move a couple of minutes later Brittain spread the ball out to Mihael Kovacevic whose pass inside was sliced by Quinn.
When the ball came out to the edge of the 18-yard box Stuart Kettlewell skied his effort well over the crossbar.
The home side were coming more into the match and a Vigurs knockdown in the box was lashed wide by Sam Morrow.
But it was the Inverness side who were controlling play in the middle of the park and County were finding it hard to create any clear cut chances.
Brittain tired a long-range effort which flew high and wide.
At the other end McKay forced a fine save from Mark Brown in the 28th minute but the breakthrough came a couple of minutes later.
Aaron Doran's cross from the right was headed down by Foran and McKay swept a stunning left foot volley past Brown from 14 yards.
The visitors were well worth their lead and Andrew Shinnie almost added a second a minute later when he fired into the side netting following a corner.
In a breakaway move in the 41st minute Quinn picked out Glen on the left and his cross into the box fell to Kettlewell at the far post but he could only stab the ball out for a goal kick.
There was action at both ends in first half injury time. Antonio Reguero pushed out a Brittain corner and Morrow's low drive was cleared off the line by Foran.
Caley Thistle broke quickly and McKay rounded Brown only for Mihael Kovacevic to get back to scoop his shot behind. From the resulting corner Foran headed wide of the far post.
County mounted the first attack of the second half and the ball broke to Vigurs on the edge of the area but his shot was straight at Reguero.
But the home side's early pressure paid off and they equalised in the 49th minute. Morrow squared the ball to Kovacevic on the right and his cutback was blasted high into the net by Quinn.
County had the bit between their teeth now and Kettlewell came agonisingly close to putting his side ahead with a looping header which just cleared Reguero's right hand post.
County were looking much more up for the fight and after Brittain and Vigurs linked on the left Kettlewell got on the end of the latter's cross but Reguero held his effort comfortably.
The visitors weathered the storm and they threatened again in the 70th minute when Andrew Shinnie tested Brown with a 25-yard shot but the County keeper got a hand to it.
But the Inverness side took the lead in the 73rd minute when a McKay shot deflected off Foran and into the net.
Just when it looked as if the visitors had the tie in the bag when Vigurs fired home a magnificent equaliser from 25 yards which flew into the net.
A Brittain free-kick in injury time evaded everyone on its way into the far corner of the net.
County looked to have booked their place in the next round but Foran popped up with an equaliser in the fifth minute of injury time when he scooped the ball into the net from close range following a Graeme Shinnie corner.