Hibs were heading for victory after Christophe Berra's 69th-minute own goal but Ikpeazu finished calmly with six minutes left to secure a 1-1 draw, halting a three-match losing streak in the Ladbrokes Premiership for Craig Levein's men.
The hosts stretched their unbeaten league run to 10 games since Paul Heckingbottom took charge but were left to rue Marc McNulty's missed penalty and a failed chance to move six points ahead of their city rivals and cut the gap on Kilmarnock to two points.
Hearts handed a first start to 17-year-old forward Connor Smith and brought in fellow teenager Harry Cochrane as Levein made four changes following the defeat by Rangers.
Edinburgh derbies are normally tight affairs but this one was open from the start with both teams committing men forward.
A number of mistakes in possession also kept defences on the back foot with Hearts centre-back John Souttar particularly culpable during the first half.
Clear chances were initially scarce until near the end of the half.
Daryl Horgan flicked a looping effort on to the roof of the net after Souttar failed to cut out Stephane Omeonga's cross, and Jake Mulraney forced a good diving stop from Ofir Marciano after a curling effort at the end of a Hearts breakaway.
Hibs came closest to breaking the first-half deadlock when Zdenek Zlamal parried Lewis Stevenson's 30-yard strike. McNulty sent the rebound towards goal but Berra cleared off the line as Darren McGregor tried to force it home.
Stevenson threatened again just after the interval with a first-time strike which was well blocked by Souttar.
The left-back continued to put Hearts under pressure when he skilfully got away from two men and delivered the perfect cross for Vykintas Slivka. But the half-time substitute headed too close to Zlamal, who produced a good stop.
Hibs got their penalty on the hour mark when Paul Hanlon nicked the ball away as Ikpeazu went to clear and was caught by the striker. But McNulty completely missed the target.
The striker wanted another spot-kick after being denied by Souttar's tackle but the defender appeared to get the tackle right and referee Craig Thomson pointed to the ball.
The breakthrough came after a one-two between Horgan and David Gray. The Irish winger delivered a low cross which hit Berra's heel and span inside the far post.
Levein made changes with Ryan Edwards coming on for his debut almost 11 months after joining from Partick Thistle.
Another substitute, Steven MacLean, set up the equaliser with good control and a cutback to allow Ikpeazu to steer the ball into the corner from 12 yards.
The Hearts goalscorer almost grabbed a spectacular winner but Marciano tipped over his overhead kick.