More aid to Iraq from the West and from the wider Arab world. Iran would be confirmed as the major threat in the region. Saddam Hussein would be viewed more as "a bastard, but at least our bastard". Iran would receive sanctions post-war, but Iraq would be unable to make any gains-- nor would Iraq's backers allow this. Instead, they'd push for a cease-fire to ensure the sought-after 'balance in the region'.
Iran would be embittered and see itself as surrounded by a hostile world. Which, given OTL evidence, would turn them even nastier. There would be probably be an American intervention in the region later on (as in OTL), but against Iran.
This would create a major mess, since lopping off Arabic Khuzestan and/or Iranian Kudistan would create problems. If added to Iraq, it would destablisise the ethno-religious balance in Iraq. If kept independent, it would prompt rattachist secessionism amongst the Kurds and/or Shi'a Arabs in Iraq.
As such, I think after Iran got beaten, it would be forced to have "democratic elections". Keeping the Ayatollah regime would be impossible, as unlike Saddam Hussein, the idea of 'bloodying their noses will be enough' would be obviously nonsensical. They'd be fanatical enemies forever, so removing them would be the only option. Any new government would be hated by much of the Iranians, and the Arabs and Kurds would still harbour secessionist dreams.
Ultimately, you get as much of a mess as in OTL.
(Actual solution would be to immediately turn around and kill Saddam, too. Hand over Sunni Iraq to Syria, in exchange for Syrian Kurdistan. Create a Shi'a Arab Mesopotamia includin Khuzestan. Create a Kurdistan out of Syrian, Iraqi and Iranian Kurdistan, and allow the Turks to forcibly expel any bothersome Kurds across the border. That would involve some bloodshed, but it would create something resembling homogeneous nation-states, so could yield a semblance of stability. But that's too sane an approach for this wishy-washy era of ours. So you get the above instead. Endless internal warfare.)
