Argentina equalised early in the second quarter when Capurro burst down the left wing and cut inside the circle and rifled the ball into the roof of the net.
But it didn’t take long for Ireland to regain the lead. From another penalty corner, Madeley was on target again.
Before half-time the Argentinians would level matters for a second time.
Demene converted a penalty corner to make the score 2-2 at the interval.
There were two goals within a minute in the third quarter. Nicolas Keenan gave Argentina the lead, converting a cross from Inaki Minadeo.
However, within sixty seconds Ireland were back level. Ben Walker received a pass from outside the circle and found Empey and he finished well to make it 3-3.
Argentina regained the lead in the 53rd minute from yet another penalty corner.
The ball was sent to Keenan at the far post and his short pass was deflected past Jamie Carr and into the net by Thomas Habif.
Tim Cross won a penalty corner for Ireland in the final seconds, but Madeley’s drag flick was saved by Thomas Santiago’s foot.