Eric Odhiambo had returned to haunt his former club when he nodded Caley Thistle into a first-half lead and the rejuvenated Highlanders looked set to hold on for the win.
But United skipper Wilkie had the final say with a late equaliser after Inverness had been reduced to 10 men when Russell Duncan was dismissed.
While Terry Butcher was keen to continue an impressive start to his tenure at Inverness, United were under pressure to bring a troubled spell of their own to an end.
As well as losing Scott Robertson to injury for the rest of the season and Willo Flood to Celtic last month, Craig Levein's men had also suffered defeat in their last three outings in all competitions.
It was no real surprise to see the Arabs boss ring the changes, with Paul Caddis handed his debut following his loan move from Celtic.
He started from the outset, along with Paul Dixon and Francisco Sandaza, with Sean Dillon, Danny Grainger and Warren Feeney all dropped to the bench following last week's Homecoming Scottish Cup defeat to Hamilton.
Inverness were unchanged from their own cup win over Kilmarnock, with Butcher looking to extend his unbeaten run to three since taking over the Caley Thistle hotseat - and match their longest unbeaten spell of the season.
United appealed for a penalty in the opening few minutes when Sandaza embarked upon a run down the left flank before setting up the shot for John Daly.
He went to ground in the box and claimed he was tripped by Pavels Mihadjuks but the appeals were half-hearted and ignored by referee Craig Thomson.
But it was Inverness who opened the scoring after 15 minutes when Dougie Imrie delivered a fine cross into the box and Odhiambo powered a header past Lukasz Zaluska.
United could have been back on level terms moments later when Daly sent a header towards goal with Wilkie waiting at the post to knock over the line but Lionel Djebi-Zadi managed to make a timely intervention.
The home side then failed with another penalty claim, this time a more convincing shout when Sandaza appeared to be brought down by Djebi-Zadi as he was about to unleash a shot.
At the other end, Ian Black tried his luck with a speculative volley from 20 yards in a bid to double the visitors' advantage before the break but Zaluska was never really troubled by the audacious attempt.
Inverness should have found the back of the net when Imrie beat Dixon to the ball and bore down on goal with only the goalkeeper to beat but, instead of taking the shot himself, he tried to tee up Mihadjuks and Zaluska was able to intercept and smother.
United were desperate to haul themselves back into the game and squandered a great opportunity shortly after the restart.
Caddis did well to shrug off his marker and cut inside from the right before whipping a teasing ball across the face of goal which was missed by both Sandaza and Wilkie in the six-yard box.
A blunder from the on-loan Celt then almost proved costly when his headed clearance landed straight at the feet of Duncan, who played the ball out to Imrie wide on the left.
Imrie gathered in plenty of space and United could only look on in relief as his powerful shot fell inches wide of the target.
United's hopes of a comeback were bolstered with 20 minutes to go when Duncan was shown a straight red card for a last-man challenge on substitute Danny Swanson as he burst clear on goal.
But 10-man Inverness could have killed the game off when Roy McBain raced past two defenders before setting up Adam Rooney only for him to produce a weak effort which was easily scooped up by Zaluska.
Levein threw Feeney and Andis Shala into the action and the latter was on the park for literally seconds when he set up the equaliser.
He met a cross from the right and flicked into the path of Wilkie who beat Esson to the ball to poke over the line from close range and secure a share of the points.