The Huthi rebels, who Tehran denies arming, were close to seizing most of Yemen when Saudi Arabia sent warplanes into its southern neighbour, with which it shares a 1,800 kilometre (1,100 mile) border.
"America's indifference to Saudi concerns and -- the other side of that coin, America's increasing interest in co-opting Iran," are among the motives behind Riyadh's action, said Professor Anoush Ehteshami, Iran and Gulf expert at Britain's Durham University.
The air campaign began last week as marathon talks between Iran and world powers aimed at ensuring Tehran never develops a nuclear bomb entered a crucial phase.
"As the nuclear negotiations proceed, the Saudis become much more nervous about America taking its eye off the Arab world by focusing on Iran," said Ehteshami.
The campaign followed urgent calls for help by Yemen's embattled President Abedrabbo Mansour Hadi, as the Huthis and allied troops loyal to ousted president Ali Abdullah Saleh closed in on his refuge in the main southern city of Aden.
Hadi, who has since fled to Saudi Arabia, denounced the rebels as Iran's "puppets", while Riyadh accused Tehran of meddling in the internal affairs of the Gulf and Yemen.
On Tuesday, Saudi Foreign Minister Prince Saud al-Faisal said that Yemen's security was "part and parcel" of the security of his kingdom and the rest of the Arab world.
Saudi Arabia 'frustrated' with US
The Huthis are not a new force in Yemen. They have fought the central government for a decade in their northern stronghold of Saada.
They also locked horns with Saudi Arabia in a previous conflict in 2009-2010.
The Huthis defeated powerful tribes in months of fighting before overrunning the capital in September, triggering condemnation -- but initially no action -- from Riyadh.
The prospect of the Huthis controlling the southern tip of the Arabian Peninsula, including stationing their forces at the strategic Bab al-Mandab strait, appears to have finally prodded Saudi Arabia into its unusual intervention.
"The Saudis have come to the hard conclusion that no one will come to their rescue if Iran manages to have a foothold in Yemen, (and) establish a kind of Yemeni Hezbollah... to practise coercive diplomacy with Riyadh," said Hassan Barari, professor of international relations at Qatar University.
Saudi Arabia is also "frustrated" by a perceived "American disengagement from the region," he said.
Signup to our newsletter and follow us on Facebook and Twitter!
Barari cited the four-year conflict in Syria where Gulf monarchies feel let down by Washington's failure to help oust President Bashar al-Assad.
Jane Kinninmont, deputy head of Middle East and North Africa programme at London's Chatham House think tank, said Saudi Arabia "views the Huthis as little more than an Iranian proxy and wants to send Iran a clear message that it faces pushback from regional powers."
The unexpected military intervention also showed that Saudi Arabia's new leader, King Salman, is ready to take drastic action to protect his country's interests.
"Saudi Arabia is no longer in a preventive mode," said Ehteshami.
"The traditional perception of Saudi Arabia being a cautious, behind-the-scenes actor is increasingly outdated. Saudi Arabia now is more of a proactive actor in the region," he said.
Setting aside differences
Riyadh has formed the largest-ever coalition of Sunni Arab countries to fight the Huthis, bringing together most of the Gulf monarchies, Jordan, Morocco, Sudan and Egypt.
The alliance is also the first that openly operates away from the auspices of Washington or NATO, though a Gulf diplomatic official said that participants would like to have international cover.
"We are working to get a UN resolution like in Mali, post-action," the official said.
It is a "coalition of the minimum" common ground, according to Barari, under which "these countries can maintain their differences but when it comes to Iran they should cast aside these difference."
Ehteshami said the Arab monarchies and Egypt could form a long-lasting bloc that would "engage Turkey and Pakistan as the new Sunni periphery of the Arab axis."
He argued that Ankara and Riyadh have put aside their "divergent" positions over Egypt's crackdown on the Muslim Brotherhood, which Turkey opposed, and are "working very closely" to push Assad out and to combat Iran's influence in Iraq.
Meanwhile, Iran is left with few options beyond condemnation.
"Iran probably doesn't want to scupper the nuclear talks for the sake of Yemen, which is not a country that is central to Iranian interests," said Kinninmont.
Ehteshami believes Tehran will pursue a traditional strategy of using proxies to wield influence.
"The Huthis are the perfect proxy for them."