The Liverpool striker, who saw his club campaign wrecked by injury and found the net just twice following his £10.5million move from Roma, demonstrated his class with a neat turn and finish 11 minutes from time in Israel.
Devis Mangia's men will now tackle Spain in Tuesday's final after the reigning champions cruised through to another showpiece with a 3-0 success against Norway earlier on Saturday.
The Jong Oranje were inches away from taking the lead with only give minutes on the clock as Adam Maher curled a free-kick over the Italy wall and against the outside of Francesco Bardi's post with the goalkeeper motionless.
Cor Pot's side went close again in a spiky and competitive first half when Ola John escaped down the left and cut the ball back for Kevin Strootman, only for the captain to fail to make a clean contact as his shot drifted wide of the target and out of reach of the lunging Maher and Georginio Wijnaldum.
Borini had half a chance on the 30-minute mark but failed to make a clean contact with his header following a cross from the right, before a rapid counter-attack ended with Ciro Immobile firing a low shot against Jeroen Zoet's legs.
Lorenzo Insigne then displayed great skill to trick his way beyond Strootman in Holland territory but showed poor decision-making as he elected to shoot from distance when he had team-mates well placed looking for a pass.
Bardi was called into action as the interval approached to fist away Daley Blind's swerving long-range effort before Luca Caldirola blocked Maher's follow-up, with play swiftly switching to the other end of the field where Borini fired into the side-netting.
The second-half was a more cautious and even affair, with few clear-cut opportunities from either side until Luuk de Jong escaped behind the Italy defence in the 70th minute only for his attempted return ball to Marco van Ginkel to go behind the reported Manchester United target.
But the breakthrough came with just 11 minutes remaining when Insigne fed Borini and the Liverpool striker skipped away from substitute Mike van der Hoorn before beating Zoet with a composed low finish into the bottom corner.
Holland pushed for a leveller as the clock ran down and the contest became increasingly fractious, but Pot's men could not find a way to get back on terms despite five minutes of added time, with Leroy Fer unable to beat Bardi after rising highest at a corner.