The hosts looked set to record a morale-boosting victory courtesy of a 65th-minute free-kick from Steven Gerrard, who now boasts nine goals in Premier League Merseyside derbies, more than any other player.
However, Jagielka levelled in sensational fashion late on, driving home a ferocious half-volley from distance to leave Simon Mignolet with no chance.
Exactly 15 years have passed since Everton's last triumph at Anfield, but Roberto Martinez's men will take great heart from the manner in which they claimed a point on this occasion.
Liverpool, once again without the injured Daniel Sturridge, were on top for much of the game, but failed to capitalise on their superiority and have now gone three Premier League matches without a victory.
With Sturridge still unavailable due to a thigh problem, Liverpool brought in Lazar Markovic and Adam Lallana at the expense of Lucas Leiva and Fabio Borini.
Everton handed a maiden Premier League start to Muhamed Besic, while Tony Hibbert featured from the off in a top-flight game for the first time in 666 days with Seamus Coleman (head) absent and there were also recalls for Kevin Mirallas and Steven Naismith.
Gareth Barry was at the heart of the action in the opening 10 minutes as Liverpool started brightly.
The former England midfielder was booked inside a minute for a crude foul on boyhood Evertonian Adam Lallana.
After Romelu Lukaku had seen an appeal for a penalty turned down following a challenge from Alberto Moreno, Barry then appeared to handle a goal-bound shot from Raheem Sterling inside the Everton area, only for referee Martin Atkinson to remain unmoved.
Barry again escaped a second booking when tripping Mario Balotelli before Tim Howard made a fine save, diving to his right to keep out Lallana's header from a corner.
Everton weathered the early storm and Lukaku tested Mignolet from long range prior to Leighton Baines delivering a dangerous low cross that Dejan Lovren did well to clear with Lukaku lurking.
Mirallas was withdrawn with an apparent hamstring injury in the 31st minute, Aiden McGeady taking his place, and Liverpool went close again before the break as Sterling forced Howard into action at his near post.
Strong defending from James McCarthy prevented Markovic from capitalising on a glorious Sterling throughball early in the second half.
With chances proving hard to come by, Liverpool boss Brendan Rodgers replaced Markovic with Philippe Coutinho on the hour mark and his side were ahead soon after.
Baines was adjudged to have fouled Balotelli 25 yards from goal and Gerrard stepped up to curl the resulting free-kick over the wall and beyond Howard, who got his left hand to the ball but could not keep it out.
Lukaku made a mess of a free header for Everton within two minutes, then Balotelli struck the crossbar from the next attack as the action switched from one end to the other.
The lively Balotelli saw an ambitious effort fly narrowly wide with 10 minutes remaining, but Jagielka found the net with an even more spectacular attempt in stoppage time to leave Liverpool stunned.
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