Shiels struck a superb hat-trick to take the tie out of the reach of Craig Brewster's side - and it could have been a more emphatic scoreline had they taken their second-half chances.
Substitute Mickael Antoine-Curier had the most glaring miss late on when he headed over in front of an empty net.
Both sides ended up with ten men when Filipe Morais picked up his second booking after an exchange with Phil McGuire, who also was yellow carded for a second time.
Paatelainen made six changes to the team that lost to St Mirren and gave a debut to Paul Hanlon at left-back with David Murphy failing a late fitness test.
But it was Hibs who made the early breakthrough to give Paatelainen a perfect start.
Hanlon and Merouane Zemmama combined and the ball broke to Shiels, who kept his cool in the area to curl the ball into the far corner of the net from 15 yards.
It was the spur Hibs needed and moments later a Morais corner broke to an unguarded Zemmama at the edge of the area and Michael Fraser had to be alert to keep it out.
But Caley Thistle showed plenty of enterprise themselves as Graham Bayne headed wide from ten yards with the Hibs defence in disarray as they pressed for the equaliser.
It was end-to-end stuff and Zemmama was unlucky when he tried to play in Morais, but McGuire managed to get a foot in to divert it to safety.
Zemmama then almost brought a second as he skipped past McGuire at the edge of the box and thumped in a terrific shot which Fraser did well to tip over for a corner.
There was a scare for Hibs when Roy McBain was given far too much space on the left and his cross picked out Marius Niculae, but the Romanian could get no power on his eight-yard shot and Yves Makaba-Makalamby gathered easily.
The Hibs midfield were guilty of not protecting their back four and Niculae caused them problems by sitting just in front of their defence.
He came close with another near-post header which Makaba-Makalamby had to keep a close eye on as it dipped just over his crossbar.
But the striker was guilty of surrendering possession after 28 minutes and Shiels played in Abdessalam Benjelloun and his angled shot slipped just inches past Fraser's left-hand post.
Hibs went two up after 53 minutes when Shiels gathered the ball at the edge of the area, slipped it through Grant Munro's legs and then produced a clinical finish.
Caley Thistle tried to get back and Ross Tokely should have done better when a Don Cowie corner picked him out but the shot was carelessly wide.
But Hibs always had the players to threaten and Morais came close to a third when he fired the ball just wide of Fraser's post.
Antoine-Curier then had an unbelievable miss when he headed a cross from Zemmama over in front of a gaping goal.
Six minutes from time, Shiels slid home his third after a shot from Morais had thumped against the post.