In fairness to Everton, a point is nothing less than they deserved as they matched Manchester United for the entire game.
Chances were few and far between for both sides in the first side and it was a failure to send off Marcos Rojo which was one of the main talking points from the first 45 minutes.
The Argentinain lunged in two-footed on Idrissa Gueye, but referee Michael Oliver only produced a yellow when a red card should have been the only outcome.
While the first half was scrappy, United managed to edge ahead of the hosts thanks to a touch of class from Ibrahimovic. The United forward received a ball over the top and with Everton 'keeper off his line to charge down the Swede, Ibrahimovic lifted the ball over Stekelenburg which just crossed the line with the aid of the crossbar.
If United were to win, they would have had goalkeeper David De Gea to thank due to a string of impressive saves in the second half.
Romelu Lukaku and Kevin Mirallas combined and the latter smashed a half-volley goalwards, only for De Gea to divert it over with an outstretched thigh.
United's best chance of the second half fell to Ander Herrera, who crashed his effort against the woodwork after Carrick had found him with a cross from the right.
Everton pushed for an equaliser. Gueye saw an effort from distance palmed away by De Gea while substitute Enner Valencia could only head an effort straight at the United 'keeper.
In an attempt to provide added solidity in the dying stages of the game, Jose Mourinho introduced Marouane Fellaini for Henrikh Mkhitaryan, but unfortunately for United, the change had the opposite effect.
Almost immediately after coming on, Fellaini brought down Enner Valencia with less than two minutes left on the clock to give away what was an obvious penalty.
Leighton Baines stepped up to take the spot kick and squeezed the ball past De Gea, who came so close to getting his right hand to the ball.
The Tofees then continued to attack after their late goal, with Baines testing De Gea once again, but the Spaniard managed to turn the full-back's powerful effort behind for a corner.
United stay sixth, but are now nine points off rivals Manchester City in fourth position and 13 points off Chelsea at the top of the league. Meanwhile, Everton stay in eighth, just one point behind today's opponents.