But in a remarkable second period in which both sides created excellent goalscoring opportunities former Murray Park midfielder Andrew Shinnie levelled with a tidy finish before his Caley teammates Billy McKay and Jonny Hayes were guilty of missing sitters.
Those squandered chances proved so costly for the visitors as Lafferty, who was excellent after replacing Alejandro Bedoya, scored the decisive goal which moved Rangers seven points clear at the top of the league until Celtic take on St Johnstone in Perth tomorrow.
On a bitterly cold day it was Caley that started the brighter of the two sides and with just two minutes on the clock McKay played the ball through to Lee Cox who, with just McGregor to beat, prodded a weak shot past the post as Lee Wallace made a sliding challenge.
It took Rangers time to get going but on eight minutes Gregg Wylde created the first chance for the Champions.
After winning a corner, the jet-heeled youngster put in a teasing cross and Ryan Esson had to be sharp to make a great stop, diving low to his right to deny Steven Whittaker who had leaped above the Caley defence.
This lifted the spirits around the stadium as did a run from Wallace which resulted in a free-kick being awarded by rookie ref Bobby Madden 20 yards from goal.
Jelavic tried his luck but the ball cannoned off the wall to the relief of Butcher and his coaching staff in the away dug out.
As expected Caley worked hard throughout and as well as being organised they had players willing and able to assist loan striker McKay in Jonny Hayes, Gregory Tade and Cox.
Cox, in particular, was proving industrious from his central berth and his driving run and superb, low cross on 33 minutes had to be booted to safety by Bartley from inside the six yard box.
The Caley players were then shouting for a penalty when a whipped free-kick was nodded on by McKay and the ball appeared to hit the hand of Jelavic.
Madden waved away the pleas but it was proving to be a good spell for Inverness with the Bears in the stadium getting restless.
A bit of urgency was required and on 42 minutes a great throw from McGregor released Bedoya on the left and the resulting tackle by Kenny Gillet produced the first yellow of the match.
Davis took and Jelavic’s looping header went wide of Esson’s far post.
At half time McCoist made his first substitution with Lee McCulloch taking the place of Edu and after just 30 seconds he was perhaps fortunate not to receive a booking for a late challenge on Hayes in the centre circle.
With the match poised both teams were giving everything to get the opening goal and on 50 minutes an intelligent through pass from Shinnie sent McKay racing clear.
He then cut back inside and, just when he was about to shoot, the forward felt his shirt was pulled by Bartley but again the ref let play continue.
With Lafferty on for the injured Bedoya Rangers came to life and Jelavic was again close with a powerful header from a low Wylde cross.
Inverness were now under real pressure for the first time in the match and on 54 minutes Rangers made the breakthrough.
Jelavic headed the ball down to Bocanegra and the American produced an excellent shot on the turn which whizzed past Esson into the net.
The US skipper injured himself in the process but was soon back on his feet and accepting the applause he deserved for his fine strike.
Lafferty certainly made the difference and, after missing a good chance himself, the Ulsterman skipped past Shinnie on the right wing and delivered a great cross which found Jelavic who was fouled as he moved away from Inverness’ goal.
The ref played advantage and Papac almost snapped the crossbar with a left foot drive which left Esson flapping at thin air.
It was now a pulsating match and on 67 minutes Caley were back in the game when substitute Andrew Shinnie found the net.
With Jelavic down and injured the visitors kept playing as opposed to rolling the ball out and when Tade beat Whittaker on the left his cross was guided into the net by the former Gers starlet.
The goal was a shock to the system for the Gers support and with the time running out Caley had two great chances to get a second goal.
Greame Shinnie again fed the ball through to McKay but after skipping past McGregor he hit the side netting with the goal gaping.
Hayes then had his hands on his head when he took the ball past the Gers keeper, but somehow failed to hit the net with Wallace clearing off the line.
With ten minutes left Caley must have wondered how they were not in front and with eight minutes left Lafferty dealt the suckerpunch blow.
Davis played in his countryman and he made the most of poor marking to drill the ball through Esson and into the net in front of a jubilant Copland Stand.
Man of the Match: Carlos Bocanegra – Defender was solid throughout and opened the scoring for his side with a great strike.