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The in-form striker was set up for a close-range finish by Gary Harkins after 86 minutes.
Ross Draper had given the visitors an early lead, rounding goalkeeper Scott Bain to finish.
Dundee dominated the second half, creating a series of good chances before the late equaliser.
In a congested mid-table, Caley Thistle were four minutes away from leapfrogging their hosts but remain in seventh place, two points behind the Dark Blues.
The Highlanders had started impressively, finding their rhythm and passing the ball crisply and accurately. Their composure was unsettling for Dundee, who spent the opening period trying to hold their defensive shape.
The visitors built much of their attacking play around Jordan Roberts, who was strong but also nimble and assured at centre-forward. By dropping off the front-line, he also joined in the build-up play and it was that versatility that led to the opening goal.
From a deep position, Roberts saw the run of Draper from deep and threaded a pass for the midfielder to collect before knocking the ball beyond Bain and knocking it into an empty net.
The home players and fans claimed for offside, in vain, and discontent grew with the performance of the officials.
The Dundee supporters spent most of the first-half booing Carl Tremarco after the Inverness full-back appeared to kick out at Greg Stewart as the pair tangled on the ground following a tackle.
Referee Andrew Dallas booked both players for the scuffle and had to keep his yellow card close to hand as he tried to manage a lively encounter.
Despite their strength in attack, Dundee struggled to create a clear chance in the first half, and the closest they came was a Stewart effort from distance that flew past.
There was a further set-back for Paul Hartley's side when defender Darren O'Dea went down injured on the cusp of half-time and failed to reappear after the interval.
Dundee were much more effective in the second period and Stewart should have equalised when the ball ran to him inside the area, but he shot wide from 10 yards out.
Rory Loy had a similar chance soon after, when he picked his way into space only for his shot to cannon off the leg of Owain Fon-Williams, the Inverness goalkeeper.
All three of the strikers were frustrated, with Hemmings blasting a volley over from Harkins' pinpoint cross-field pass.
Having been booked in the first-half for time-wasting, Fon-Williams barely had a moment's respite. His sharpness in racing off his goal-line after Gary Warren's miscued header flew straight to Stewart, prevented an equaliser, since the striker's effort flew straight into the keeper's body.
It looked then as if Dundee were going to be thwarted, but a striker as prolific as Hemmings only needs half a chance and he took his when Harkins headed a corner back across goal. Hemmings was first to react and he steered the ball home.
Kane Hemmings struck his 20th goal of the season as Dundee hit back against Inverness CT to preserve their place in the top half of the Premiership.