Victor Obinna and Dmitri Sychev struck in quick succession to turn the contest on its head after Imre Szabics had put the home side in front.
The Austrian champions have endured a slow start to the new campaign, having failed to reach the group stage of the Champions League, losing to BATE Borisov in the play-off, and losing two of their opening seven league games.
And they were second best throughout to leave themselves facing an uphill task if they are to progress from a tough group which also includes Anderlecht and AEK Athens.
The start of the match was delayed for 40 minutes by floodlight failure at the UPC-Arena and when play did get under way Lokomotiv were the quicker to settle.
Dennis Glushakov headed wide from Maicon's cross before going for goal himself and seeing his long-range effort parried by Sturm goalkeeper Silvije Cavlina.
But the Austrians took the lead against the run of play in the 14th minute.
Patrick Wolf crossed from the right and Szabics slammed a shot into the top corner at the near post.
But the visitors turned the game around just before the half-hour mark.
Obinna grabbed the equaliser, converting with a low finish from close range following Roman Shishkin's corner.
And Sychev put the visitors in the driving seat when he reacted quickest when Glushakov's 30-yard strike came back off the bar and volleyed the rebound into the net.
The Russian side were now firmly in control and only Cavlina prevented them from extending their lead soon after the break, parrying Alberto Zapater's shot.
The influential Glushakov then fired over from six yards and former Manchester City striker Felipe Caicedo brought a save out of Cavlina as the visitors continued to pose the greater danger.
Manuel Weber worked Lokomotiv keeper Guilherme with a long-range effort in stoppage time, but Sturm never looked likely to find a way back into the game.