Ipswich remain firmly rooted to the bottom of the Championship despite picking up a point from promotion-chasing Sheffield United.
Town are four points from safety while the Blades occupy the final play-off spot.
Sharp almost put United in front in the second minute when he was freed up on the edge of the penalty area and his right-footed shot was turned out for a corner by Ipswich goalkeeper Dean Gerken.
Six minutes later good build-up down the left involving former Ipswich forward David McGoldrick and full-back Enda Stevens resulted in a cross which was narrowly headed over the bar by Sharp.
Incessant pressure from the visitors led to a free-kick just outside the penalty area in the 16th minute which was cleared by the Ipswich defence.
Two minutes later Sharp had the ball in the net following a free-kick by Northern Ireland international Oliver Norwood but was ruled offside.
Harrison had a half chance following a cross from raiding full-back Jordan Spence but his header was straight at goalkeeper Dean Henderson.
Luke Chambers then had the ball in the net in the 35th minute following a corner by Jon Nolan but the Town centre-back was ruled to have committed a foul by referee Andy Woolmer.
And against the run of play Ipswich took the lead.
A mix-up in the Sheffield United defence led to the ball falling to Freddie Sears wide on the left.
He found Harrison free outside the penalty area and his forward motion carried him inside the box where his rasping right-footed shot took a slight deflection off John Egan and resulted in the ball flying into the back of the net past Henderson.
Two minutes into the second half a right-wing cross by Norwood found Sharp inside the six-yard area and he headed firmly past Gerken.
A timely challenge by Matthew Pennington on George Baldock in the 66th minute led to a corner taken by John Fleck which was headed narrowly wide by Egan.
In the 69th minute both sides brought on their first substitutes with Leon Clarke replacing McGoldrick and Grant Ward coming on for Andre Dozzell.
Sheffield United were dominating play as the game entered the final 15 minutes and Ipswich introduced Jordan Roberts in place of goalscorer Harrison just before Clarke headed over the bar.
Eight minutes from time Trevoh Chalobah was involved in a collision with Norwood which resulted in the Blades midfielder receiving a yellow card.