Jordan Pickford was tested early on, but Defoe gave them the lead in the 34th minute to round of a decent half for the Black Cats.
Duncan Watmore had early second-half opportunity, before the lights went out at the Stadium of Light. Anichebe added a second once the game got back underway, and sealed the win with six minutes to go to secure another vital three points.
Tested early on
Sunderland fans were optimistic ahead of the visit of Mike Phelan's side, after their first win of the season before the international break, but it was the visitors who had the brighter start.
The first chance for the Tigers came just two minutes in, Dieumerci Mbokani beat his man his ease, and looked to have bettered Pickford with his low effort, but the young keeper did well to put it wide.
They had another sniff at goal in the 19th minute, with Samuel Clucas stinging the palms of Pickford from the edge of the area, and the 22-year-old did well to palm it away.
150 not out
Defoe was the hero last time out, with his penalty securing the win over Bournemouth, and he was the hero in this one opening the scoring with his historic strike.
It was an excellent piece of individual play from the veteran striker, as he wriggled his way into the area. The extra touch proved to be the vital one, as he rifled it into the bottom corner to send the Stadium of Light into a frenzy.
The lights are out
The Black Cats came flying out of the traps in the second period, and had a great opportunity to add a second just a minute after the restart.
Billy Jones' cross was flicked on by Defoe into the path of Watmore, who was looking to add to his spectacular goal on international duty midweek, but it was straight at David Marshall.
Something that many weren't expecting came next, as the light was taken out of the namesake stadium, but much to the relief of Moyes, the game back underway after a ten minute delay.
Ryan Mason had a good opportunity after the restart, the midfielder had time and space on the ball to get his shot away from 12 yards out, but it was just wide of he far post.
Sunderland began to dominate the proceedings across the pitch, and the points looked sealed when they added a second goal just before the hour mark.
Anichebe had been performing well over the last few weeks, and he showed his strength on this occasion, the striker stepped inside his marker before lashing it past Marshall at the near post.
Pickford was called upon almost instantly, Robert Snodgrass' effort looked to have looped beyond him in the 64th minute, but the Washington-born keeper was at full stretch to keep it out.
Hull's best chance came in the 78th minute, and it was a sight to behold. Curtis Davies' header was brilliantly saved, before Mbokani's effort was cleared off the line, and Jake Livermore's strike was blocked.
Rounding off a great performance
It had arguably been Sunderland's best performance of the campaign, and that was certainly secured with their third goal in the 84th minute. Defoe continued his budding relationship with Anichebe as he played it through to the 28-year-old. Anichebe's first touch was excellent to get away from the defender, and similar to his first he struck it home at the near post.
The performance ended on somewhat of a sour note, as the Black Cats were reduced to ten men. It was poor from Papy Djilobodji, as he went in clumsily on Jarrod Bowen, and Lee Mason had no option but to give him his marching orders, but the day belonged to the Black Cats.