The Toffees defender has welcomed the return to fitness of the ex-Manchester United player, commending him as an unsung hero in the side's midfield after victory over Tottenham
Having seen his fine start to the season cut short by a thigh injury, Gibson had been forced to watch much of this campaign from the sidelines, but the fit-again Irishman has been restored to the Toffees midfield for their last three fixtures, much to the delight of stand-in captain Jagielka.
"Maybe Darron hasn't scored that many since he has been here; he's not a dribbler and not what you'd see as a ‘fancy Dan’ sort of player," the 30-year-old told reporters.
"But if you filmed his role in the team and watched it back there would be some fantastic passes, great tackles and some clever football.
"He came from a great club in Manchester United and it shows with the time he finds on the ball and the confidence he has in long-range passes.
"It makes playing against us a lot harder when you have people like Darron in the team and Ossie [Leon Osman] by the side of him. They are two different footballers but equally as important.
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"Gibbo is massively important for us and you need to have someone who can keep the opposing defence on their toes. We know that if he does get a bit of time he can be like our quarterback and start putting in some fantastic passes."
Though his side currently sit fourth in the Premier League table, Jagielka admitted his frustrations at their recent run of seven draws in their last 10 league games, and hailed the importance of Sunday's win.
"We would have swapped four draws for two wins and two defeats," he added. "It's all about getting wins in this league.
"Don't get me wrong, it's nice to stay unbeaten. Going to Man City and drawing is a good point and a draw at home to Arsenal is, too. But other games where we have not managed to kill off teams have been very disappointing.
"It wasn't make-or-break against Spurs but it was desperately important for us to pick up three points."