In any case, the Persians had some cavalry that was in contact with the first Greek units to arrive, but Alexander led the elite Companions on an outflanking charge while the Macedonian foot companions covered the rest of the battle column as it formed up against the Persians. The Macedonian line was arrayed with the heavy Phalanxes in the middle, and cavalry on either side.
The battle started with a cavalry and light infantry feint from the Macedonian left, from Parmenion's side of the battle line. The Persians heavily reinforced that side, and the feint was driven back, but at that point, Alexander led the horse companions in their classic wedge-shaped charge, and smashed into the center of the Persian line. The Persians countercharged with a squadron of nobles on horse, and accounts show that in the melee, several high-ranking Persian nobles were killed by Alexander himself or his bodyguards, although Alexander was stunned by an axe-blow from a Persian nobleman. Before the noble could deal a death-blow, however, he was himself killed by Clitus the Black. Alexander quickly recovered.
The Macedonian cavalry then turned left and started rolling up the Persian cavalry, which was engaged with the left side of the Macedonian line after a general advance. A hole opened in the recently vacated place in the battle line, and the Macedonian infantry charged through to engage the poor quality Persian infantry in the rear. At this, both flanks of the Persian cavalry retreated, seeing the collapse of the center. The infantry also routed, with many being cut down in the rout.
Total casualties for the Macedonians were anywhere between 100 and 200. The Persians had 2000 infantry captured, roughly 1,000 cavalry and 3,000 infantry killed, mostly in the rout.
Modern historian Peter Green suggests that the varying accounts of the battle and the seemingly suicidal battle order of the Persians (the cavalry defending a river where they could not charge and quality Greek mercenaries in the rear where they were no use in the battle) was due to a cover-up by Alexander of an initial defeat. According to Green’s version, Alexander disregarded Parmenion’s advice and immediately attacked the Persian’s position. The steep riverbank was (properly) guarded by infantry that rained javelins down upon Alexander and his forces, who were badly mauled and forced to retire. Alexander then grudgingly accepted Parmenion’s advice, crossed the river during the night in an uncontested location, and fought the battle at dawn the next day. The second battle at Granicus was generally as described in the sources (without the river crossing). This would make sense out of the Persian’s nonsensical order of battle. The Persian cavalry would hurry to the location of Alexander’s night crossing and reach the scene of the battle first, with the slower infantry struggling in the rear to catch up with the battle. Even if Alexander eventually won the battle, he would have had ample motivation to cover up his first initial defeat on Asian soil, and he would be loath to admit that he was wrong and Parmenion was right.