They gunned down three soldiers at the entrance to Sayun airport in southeastern Hadramawt province, which is also used by the air force, before capturing the control tower and other parts of the facility.
Another five soldiers died in a simultaneous suicide bombing at a nearby military headquarters.
Nine civilians, including a woman and her two children, were killed and eight others were wounded in a suicide attack by the militants at a date packing plant, en route to the airport, the defence ministry said.
Troops retook the airport, killing six militants and freeing hostages seized from the control tower.
Four militants were captured, and others fled.
The assault took place as a Yemen Airways plane landed, a military official said.
Troops scrambled armoured vehicles to confront the militants and evacuate the flight's passengers in army buses through the northern gate of the airport.
Sayun is the main town in the Hadramawt valley, a jihadist stronghold in the province's interior.
Hadramawt's rugged terrain provides hideouts for militants of Al-Qaeda in the Arabian Peninsula, considered by Washington as the jihadist network's most dangerous affiliate.
On May 24, militants launched a massive pre-dawn assault on Sayun, in which they attacked police and army bases and public buildings with suicide bombers, rocket-launchers and heavy machine-guns.
Before withdrawing, they also ransacked the main post office and two banks.
The assault killed 15 soldiers and police. Twelve militants also died, three of them suicide bombers.
President Abdrabuh Mansur Hadi, fired Sayun army commander General Mohammed Somali over that attack, replacing him with one of his own loyalists, General Ahmed Ali Hadi.
He had ordered security forces on high alert nationwide, including in the capital, after the army launched a ground offensive against Al-Qaeda in late April in two southern provinces further west -- Abyan and Shabwa.
The operation aims to expel the militants from smaller towns and villages in the two provinces that escaped a previous sweep in 2012.
Hadi has vowed to press the offensive until jihadists are eradicated from all of Yemen's territory.
Taking advantage of a collapse of central authority during a 2011 uprising that forced Hadi's predecessor, veteran strongman Ali Abdullah Saleh, from power, Al-Qaeda seized swathes of the south and east.
Although government forces have captured several major towns, analysts say the army's gains may have been the result of a tactical retreat by Al-Qaeda in coordination with Yemen's powerful tribes.
The army says 500 Al-Qaeda militants have been killed in its latest operation, while 40 soldiers have died.
Al-Qaeda has launched a spate of spectacular attacks on army headquarters around the country in recent months.
In December, it assaulted the defence ministry in the heart of the capital, killing 56 people.
An April attack on army headquarters in the main southern city of Aden left at least 20 people dead.
AQAP has also been targeted in an intensifying drone war this year.
The United States is the only country operating drones over Yemen, but US officials rarely acknowledge the covert operations.
Around 60 suspected jihadists’ were killed in a wave of strikes against AQAP bases and training camps in mid-April.
The drone programme has been defended by both the White House and Hadi, but has been sharply criticised by human rights groups for its civilian toll.