Laursen steered Dirk Kuyt's low cross into his own net in the first half, but Barry levelled from the spot five minutes from time after Jamie Carragher handled in the penalty area.
However, a moment of magic from Gerrard two minutes later ensured the three points went to the visitors.
Fernando Torres could not mark his competitive debut with a goal, despite a lively performance from the £20million man, but Rafa Benitez will be happy after a solid display from his side.
Villa started positively and Craig Gardner fizzed an early effort at goal before Torres showed the away fans the first glimpse of his talent as he burst beyond the Villa defence before firing his shot just over.
Reds skipper Steven Gerrard then forced a save from Stuart Taylor and Olof Mellberg needed to be alert to clear Jermaine Pennant's cross with Torres lurking.
Liverpool started to take a grip on the game and Torres skipped past Laursen only to pull his shot wide before Liverpool took the lead in comical circumstances in the 31st minute.
Torres was again involved as he saw his effort superbly saved by Taylor from point-blank range, but when Dirk Kuyt dragged the ball back across goal Laursen turned the ball into his own net from six yards.
Confidence clearly flowed through Liverpool after taking the lead and Gerrard lumped the ball over when he should have tested Taylor.
Stiliyan Petrov had a sight of goal for Villa but shot straight at Jose Reina and Ashley Young shot weakly over the bar when presented with a chance on the volley.
Liverpool should have extended their lead in the second half but Gardner produced a brilliant block to deny Gerrard a certain goal and Liverpool substitute Ryan Babel should have marked his debut with a goal a minute after entering the action, but blazed wastefully wide.
When Barry levelled from the spot with a classy penalty it looked like the home side had snatched a draw, but Gerrard would have the final say with a brilliant 30-yard free-kick three minutes from the end.