Second-placed Wales can still win Group D - and automatic qualification to next summer's World Cup finals in Russian Federation - if they overcome the Republic of Ireland in Cardiff on Monday and leaders Serbia fail to beat Georgia at home on the same evening.
Murphy broke the deadlock after seizing on a flicked-on long throw after just two minutes, and made it two before 20 minutes were out.
Depending on Monday night's results, Wales could qualify for Russian Federation 2018 automatically, go into a play-off, or miss out altogether.
Ireland, who led Group D early on before three points in their previous four games pushed them back to third place, trail Wales by a point ahead of the decider against their near neighbours in Cardiff on Monday.
"We've got 90 minutes in which to try and get a goal", said O'Neill, who welcomes Brady and fellow winger James McClean back from suspension. Fresh from signing a new two-year deal with the Football Association of Ireland, Martin O'Neill selected Callum O'Dowda in the starting XI, who became the youngest player to start a competitive worldwide under the Irish boss.
Surprise semi-finalists at Euro 2016, Wales have not played at a World Cup Finals since 1958 and could finish a qualifying campaign unbeaten for the first time in their history.
Wales and Ireland head into a winner-takes-all encounter at the Cardiff City Stadium.
"In my mind, he's as big a loss to us as he is to Wales".
In the first half, Wales was only able to create some opportunities that could bother Georgian goalkeeper, Giorgi Loria.
The Republic of Ireland's Callum O'Dowda competes with Moldova's Petru Racu during their Group D match at the Aviva Stadium last night. "I wasn't sure I would get used to global football, but qualification for the Euros made it all worthwhile", he said.
Meanwhile, the key men for the visitors are Jeff Hendrick and skipper David Meyler, who will have the task of neutralising the threat of Aaron Ramsey, while Ciaran Clark and Shane Duffy will aim to keep Sam Vokes quiet. Subs: Arter 6, McGeady 6, Maguire 6. Moldova: Cebanu (GK), Racu, Epureanu (C), Ionita, Gatcan, Dedov (Cociuc 55), Ginsari, Bordian, Platica (Ambros 78), Anton, Rozgoniuc. Subs: Cociuc 6, Ambros 6. Despite notable contributions in the move by global team-mates Robbie Brady and Stephen Ward, it's hardly the type of goal he is likely to score for Ireland - it featured 24 passes.
27' - PLATICA SHOT - Platic leathers a volley at goal, and Randolph is on hand to fly to his right and tip it away from goal. For once, he picked the wrong pass when through on goal and in the box, the move eventually ending with Long trying to pick his spot in an open net, only for it to drop wide.
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