Steven Gerrard had put Liverpool ahead with a second-half free-kick, but he was upstaged in injury time when his former England colleague Jagielka drove an exquisite half-volley into the top-right corner from 25 yards.
The 32-year-old’s memorable strike prevented Liverpool from provisionally climbing to sixth place in the table and means that Brendan Rodgers’s side have now gone three league games without victory.
“It has been a frustrating season so far, so to go 1-0 down and keep knocking at the door showed tremendous character. We need to keep showing character,” Jagielka told BT Sport.
“The lads need to keep playing the same way, keep having the courage to do the right things, and hopefully this will be a kick-start to the season for us.”
Bidding to halt a run of consecutive defeats, Liverpool quickly took control of the 223rd Merseyside derby and should have had an early penalty when Gareth Barry blocked a Raheem Sterling shot with his arm.
Everton goalkeeper Tim Howard produced smart saves to thwart Mario Balotelli, Adam Lallana and Jordan Henderson, while the visitors lost winger Kevin Mirallas to an apparent hamstring injury on the half hour.
Roberto Martinez’s side held out until the 65th minute, when Gerrard stepped up to bend a 22-yard free-kick into the top-right corner after Balotelli had been felled by Leighton Baines.
Moments later Howard diverted a close-range volley by Balotelli onto the bar and in injury time Jagielka snatched a point for the visitors with a goal destined to enter derby folklore.
Aiden McGeady’s left-wing cross was headed out by Dejan Lovren and Jagielka met it with a beautiful first-time strike from outside the box that ripped past home goalkeeper Simon Mignolet.
The two teams remain locked in mid-table as a result, with Liverpool a point above their neighbours.
Saturday’s action concludes with another local derby, as Tottenham Hotspur cross north London to tackle arch rivals Arsenal.
Beforehand, leaders Chelsea will look to preserve their unbeaten record when they host third-place Aston Villa.
Champions Manchester City visit Hull City, while Manchester United will hope to return to winning ways following their 5-3 defeat at Leicester City when they host West Ham United.