Jones (left) celebrates what could prove to be a crucial away goal for the Welsh side
Motherwell boss Jim Gannon suffered an embarrassing defeat by Llanelli in Europa League qualifying in his first match in charge of the Scottish club.
The Steelmen enjoyed plenty of the ball early on, but were stifled by some stiff Welsh resistance.
Llanelli took a shock lead on 28 minutes on a rare foray forward, when Stuart Jones headed in from a corner.
Motherwell tried to get back in the match but looked disjointed and could not convert any of their chances.
The defeat means Motherwell go to Parc y Scarlets in a week's time looking to salvage their Europa League future.
Gannon had to deal with the loss of nine regulars from last season's first-team squad, but his side still looked good in the opening exchanges, and with just five minutes on the clock should have taken the lead through Jamie Murphy.
The midfielder beat Llanelli's offside trap to collect a ball over the top from Ross Forbes, but instead of shooting himself he tried to square to John Sutton, allowing the visitors to regroup and clear.
The Welsh Premier League runners-up were unsettled in the centre of defence when in quick succession, Stuart Jones was booked for a rash challenge, then Lee Jarman was forced to leave the field injured.
For all their possession, Motherwell found it difficult to break down a resolute 11-man defensive unit, which served to frustrate the hosts and mute their fans.
On the rare occasions that the ball reached Reds striker Rhys Griffiths he found himself isolated with no supporting outlet.
But the Welsh side took the lead against the run of play through Jones on 28 minutes.
Fraser conceded a goal on his Motherwell debut
The home side conceded a corner defending player-manager Andy Legg's long throw, and from the set piece Jones stole in at the back post to bundle a header past goalkeeper Michael Fraser.
Motherwell attempted to press from the wide areas, but their delivery into the box left a lot to be desired, and they were booed off the Airdrie pitch at 1-0 down at the break.
After the restart, the Steelmen's play exhibited more pace and purpose, with O'Brien looking sharp on the right.
His play set up Steven McGarry then Sutton with headers, although neither could convert, and before long the urgency had fizzled out of the hosts' game.
Murphy shot wide from a volley, and substitute Paul Slane also went close with a drive before, with seconds remaining, forcing Llanelli goalkeeper Ashley Morris to make his first serious save of the match with a fine strike.
Forbes also had one last effort which Morris held easily, but it was too little too late from Motherwell, and the Welsh club held on for a memorable victory, much to the disgust of the home support.
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