Two Sanchez strikes and an Aaron Ramsey goal put the visitors firmly in control in the first half, before Stephen Quinn gave Hull hope on 56 minutes, but the Gunners held on.
Arsenal are now unbeaten in 10 games and, still with a game in hand, they have equalled City’s 70 points, albeit with an inferior goal difference.
The win also secured Arsene Wenger’s side a place in the Champions League for the 18th successive season.
Hull remain level on points and goal difference with Leicester in the battle for Premier League survival, but have dropped beneath them having scored fewer goals.
Sanchez, who has now scored in all three meetings with Hull this season, pick-pocketed Tom Huddlestone in midfield after 28 minutes to instigate the opener. Jake Livermore brought him down to prevent an ominous dribble towards goal, but Sanchez’s 25-yard free-kick sailed past a helpless Steve Harper, via a fortuitous deflection off Michael Dawson.
Five minutes later, Santi Cazorla pinged a missile of a pass with his left foot from the half-way line, picking out the onrushing Ramsey perfectly. The Welshman, who had seemed certain to be substituted earlier after an ankle injury, controlled it and beat Harper with another deflection benefitting the visitors.
While Hull had their moments in the first half – Sone Aluko sent a feeble header off target from a few yards out after Robbie Brady’s left-wing cross – Arsenal put the game beyond them before the interval.
Sanchez had been denied by Harper after Cazorla sent him scurrying through on goal but, presented with an identical chance seconds later, he wouldn’t miss again. Ramsey played in Sanchez, who rounded the goalkeeper for his side’s third.
Quinn, who had threatened with a first-half header, gave Hull hope by converting a similar chance on 56 minutes. Huddlestone centred the ball and the Irishman scored his first Premier League goal in eight years.
Although Hull rallied admirably following their goal, Arsenal continued to illuminate the match with some stunning interchange in the final third. One such move was highlighted by a quite remarkable back-heeled volley by Mesut Ozil which set up a dangerous Sanchez move down the left.
Jack Wilshere’s return as a 68th minute substitute in place of Ramsey was another major positive for Arsene Wenger ahead of the final three games of the season. His first involvement was a trademark burst out of midfield to win a free-kick but although the manner of his acceleration evoked memories of old, his fall was worrying until he immediately climbed to his feet.
Wilshere nearly crowned his return with a goal when Hector Bellerin’s initial shot was kept out by Harper and his close-range rebound was kept out by James Chester. As Wilshere appealed for handball, Sanchez bundled the loose ball wide.
The England midfielder continued his impressive cameo with a quick dash down the right wing that may have resulted in a penalty after he fell under Chester’s challenge. A fellow England international returning from a serious injury, Theo Walcott, only got four minutes but a side-footed effort drifted wide before Sanchez’s hopes for a hat-trick evaporated when he shot wide as Arsenal counter-attacked in stoppage time.
Arsenal have now won 18 of their past 21 games, and host Swansea next as they aim to take advantage of their extra match over City.
Hull: Harper 6, Chester 6, Huddlestone 5, Brady 7, Livermore 5, McShane 5, Dawson 5, Aluko 5, Elmohamady 7, N’Doye 6, Quinn 6.
Subs: Meyler 6, Jelavic 6, Robertson 6.
Arsenal: Ospina 6, Bellerin 7, Mertesacker 7, Koscielny 7, Monreal 7, Coquelin 7, Cazorla 8, Ramsey 7, Ozil 7, Sanchez 8, Giroud 6.
Subs: Wilshere 7, Walcott 6.
Man of the match: Santi Cazorla.