The hosts entered the day in fifth position and were looking to boost their top-four hopes against a Black Cats side rooted to the foot of the Premier League table.
Everton had most of the early possession and pressure but the game turned on its head in the 23rd minute when midfielder Ki was brought down by Howard inside the penalty area and the American received his marching orders.
Ki stepped up to take the spot kick himself and calmly slotted the ball beyond substitute stopper Joel Robles.
At the other end, Sunderland keeper Vito Mannone was in inspired form, denying Phil Jagielka, Bryan Oviedo and Ross Barkley on a day of frustration for the home side.
The Black Cats' defence was key, keeping their second clean sheet in as many games, as they made their extra man advantage count. They largely limited Everton to long-range efforts and even though the second-half introduction of Ross Barkley boosted the Toffees, not even he could find a breakthrough.