The 17-year-old's first senior goal with six minutes to go cancelled out Richie Foran's penalty, which gave the hosts the lead mid-way through the second half of Saturday's clash at the Caledonian Stadium.
Inverness's Owain Tudur Jones was dismissed in the 53rd minute and Aberdeen captain Russell Anderson was given his marching orders 13 minutes later, both for dangerous challenges.
The Highlanders slipped to the bottom of the Scottish Premier League prior to kick-off following St Johnstone's lunchtime victory at home to Celtic.
On-loan Celtic defender Andre Blackman made his Caley Thistle debut, replacing Shane Sutherland as the only change to the side beaten 4-1 at Motherwell last time out.
Aberdeen also made one change to the side who drew 0-0 at home to St Mirren two weeks ago with Ryan Jack in for Isaac Osbourne.
Andrew Shinnie was the first to test visiting goalkeeper Jamie Langfield, who stopped a 20-yard effort.
Aaron Doran was booked after tugging back former Inverness striker Jonny Hayes, who received boos from some home supporters as he faced his ex-employers for the first time.
Jack's shot on the half-hour was deflected wide by Josh Meekings as Aberdeen started to pile on the pressure.
A dangerous Hayes cross was headed wide by Meekings in front of his own keeper Ryan Esson.
Hayes then set up Stephen Hughes, whose shot was blocked by a sliding Ross Draper tackle, before Scott Vernon connected with a Ryan Fraser crossed but saw his header went just wide.
Meekings was booked just before the interval for fouling Hughes.
Although the Dons were in the ascendancy they failed to put anything on target and the sides were all square at half-time.
That soon changed when moments after the restart a Hayes corner was sent goalbound by Andrew Considine, who slid in at the back post, only for it to be blocked on the line by a wall of bodies before being smothered by Esson.
Inverness responded with a 30-yard thunderbolt that went inches wide from Blackman.
Caley Thistle were reduced to 10 men when Tudur Jones fouled Fraser in the 53rd minute.
It was the Welsh midfielder's second straight red card of the season, after being dismissed in his side's first home game against Kilmarnock.
Attacker Andrew Shinnie was sacrificed for Sutherland as Inverness aimed to tighten their midfield.
The substitute was fouled from behind in the box moments later by Dons captain Anderson, who was also given a straight red.
Caley Thistle captain Foran beat Langfield from the spot in the 67th minute.
Foran then played in Doran who might have doubled the lead if not for a last-ditch tackle from Mark Reynolds.
Aberdeen responded with an equaliser from Smith who sent a glancing header past Esson from six yards out in the 84th minute.
Sutherland was stretchered off late on following a challenge from Smith.