Kilmarnock briefly threatened to take something out of this match when Darren Barr struck from close range in the 76th minute - but they could not find an equaliser.
David Raven was still out with a groin problem, while James Vincent remained sidelined with a knee injury.
Visitors Killie made just the one change from the side which beat Hearts 2-0 last weekend, with Rory McKenzie taking the place of Barry Nicholson, who dropped out altogether.
Rabiu Ibrahim was again not involved for Killie after collapsing during the 2-0 win over Ross County last month.
Killie were seeking a third consecutive victory and Manuel Pascali had an early drive from 22 yards that was straight at Inverness goalkeeper Dean Brill.
Watkins' cross found Billy McKay, who touched it back into Doran's path and he found the target from 18 yards via a deflection off Sean Clohessy, which deceived goalkeeper Craig Samson.
Kris Boyd has been in good form for Killie of late and he came close to hitting an equaliser after good work by Jeroen Tesselaar, but his drive from the angle of the 18-yard box fizzed over Brill's crossbar.
The better opportunities were falling the way of the home side and Ross Draper had a chance to double their lead - only to shoot over the bar after Watkins had done well to tee him up.
Killie were presented with their best chance as the interval approached. Brill's misplaced pass was seized upon by Michael Gardyne, but the forward took too long to make up his mind as what to do, allowing Foran to come back and make a timely clearance.
That missed opportunity would be one that Kilmarnock would rue just seven minutes into the second half as Caley Thistle doubled their advantage.
A wonderful, free-flowing team move eventually saw Foran's incisive pass release Shinnie, who cut past Darren Barr, before curling a lovely effort past Samson from 14 yards.
However, the visitors gave themselves a lifeline with 14 minutes of the contest remaining, when Barr escaped the attentions of his marker to turn home an inswinging free-kick from substitute Sammy Clingan.
As quickly as they had reignited hopes of a comeback, the visitors almost fell two goals behind again - but the upright kept out a Nick Ross header after he had done well to connect with Doran's cross.
Five minutes of injury-time saw Killie push forward in search of an equaliser, but Inverness remained resolute to see the game out.
- Sports & Recreation
- Darren Barr
- Aaron Doran
- Graeme Shinnie