Hemed scored his first-ever goal for the visitors from a penalty on 34 minutes after Miguel Flano had felled the Israeli just inside the area.
Garcia then headed the hosts level in first-half injury-time when he was left unmarked inside the six-yard box from Alvaro Cejudo's corner and he repeated the trick 15 minutes into the second period as he again met a Cejudo corner to flick a header past Dudu Aouate.
Mallorca were reduced to 10 men in the 72nd minute as Emilio Nsue was shown a straight red card for kicking out at Roland Lamah, but they were given a second penalty only minutes later as Lamah appeared to clip the heels of Alejandro Alfaro and Hemed stepped up again to claim a point for his side.
The visitors arrived in Pamplona at the end of a turbulent week that saw Michael Laudrup resign as manager, but with interim boss Miguel Angel Nadal in charge they looked bright in the early stages with Tomas Pina and Nsue both having efforts palmed away by Andres Fernandez.
Osasuna grew into the game after the opening quarter and went close to taking the lead themselves when Lamah's fierce effort was turned away by Aouate at the near post.
The hosts went ahead after Flano's clumsy challenge through the back of Hemed saw the referee rightly point to the spot and luckily for the Osasuna defender only produce a yellow card.
Hemed had not scored in an underwhelming start to his career in Spanish football but he showed plenty of poise to calmly wait for Fernandez to move to the right before slotting the ball into the bottom left-hand corner.
Osasuna's first equaliser was thanks to some awful defending by the visitors as Garcia was given a free header inside the centre of the six-yard box and the on-loan Atletico Madrid midfielder made no mistake by powering his header high past Aouate.
Unbelievably Mallorca did not not learn their lesson and committed the same mistake on the hour-mark as from another Cejudo corner Garcia found space to glance a header into the far corner.
The hosts were in control at that point and appeared to have the game sewn up when Nsue stupidly lashed out at Lamah and was dismissed.
However, Lamah then unnecessarily clipped Alfaro's trailing leg as he sped into the box with 10 minutes remaining to concede another penalty. Hemed took responsibility once more and again sent Fernandez the wrong way to bring Mallorca level.
Osasuna did not do nearly enough with the extra man in the final 10 minutes as Mallorca were happy to see the game out and pick up their first point away from home this season.