Steve Bruce's team had surged into a 2-0 lead when the teams met at Wembley in last season's final before the north London club secured a 3-2 extra-time triumph to lift the famous trophy.
But Hull were unable to worry Arsenal in the same manner during the opening stages this time, and the hosts were good value for Mertesacker’s headed opener.
Alexis, Nacho Monreal and the returning Theo Walcott all went close to doubling the lead before the early inventiveness faded from Arsenal’s play.
Arsene Wenger's men still largely retained control of the contest and Alexis sealed a deserved return to winning ways eight minutes from time, following their Premier League reverse at Southampton on New Year's Day.
Walcott returned to the Arsenal starting line-up for the first time since he tore knee ligaments in last year's third-round win over Tottenham, and the England man was joined by Alexis and Joel Campbell in a pacy forward line.
Hull manager Bruce made wholesale changes, with Curtis Davies the only player retained from the 2-0 Premier League win over Everton.
Veteran Hull goalkeeper Steve Harper saved smartly from Campbell after the Costa Rica international exchanged passes with Alexis in the fourth minute.
Walcott and Alexis then combined for the latter to lob a shot onto the roof of the net - Hull defender Harry Maguire blocking an initial effort.
Tom Ince cut in from the right to thump a low shot past the near post for Hull, but his team were behind in the 20th minute, Mertesacker towering to head home an Alexis corner.
Arsenal immediately looked to press home their advantage, with Paul McShane brilliantly clearing off the line after Alexis had rounded Harper, and the goalkeeper diverted Monreal's near-post header from the resulting corner onto his near post.
Harper thwarted Walcott in the 27th minute on the end of a superb chipped pass from Santi Cazorla but Arsenal failed to retain their earlier fluency.
Campbell jinked his way past Davies and tried to guide the ball into the bottom corner four minutes into the second half, but Harper was able to hold a tame strike.
The forward came up short once more in the 61st minute, pulling a left-footed shot wide when confronted by a sprawling McShane.
Maguire then produced a magnificent last-ditch challenge to deny Alexis, before Walcott became the latest Arsenal attacker to spurn an opening, stabbing the ball wastefully wide having been played through by Cazorla.
Harper scrambled out to save from Alexis in the 74th minute, the former Barcelona forward losing his footing at the crucial moment, before substitute Alex Oxlade-Chamberlain failed to convert Alexis' drilled cross.
The Chile star got the goal his efforts deserved with time running out, collecting Cazorla's pass and swivelling on the edge of the box to curl a low strike past Harper.
The result retains Arsenal's hopes of becoming the first team since Chelsea in 2010 to retain the FA Cup.
