An even opening few minutes was punctuated by a flicked shot from Latics striker Chris Killen that forced a low save from goalkeeper Darryl Flahavan.
But Southend responded with Mitchell Cole shooting wide before the winger set up the Blues' opening goal two minutes later. His cross into the six-yard box was met at the far post by Lawson, who rose highest to head home on ten minutes.
The hosts then stepped up the pressure with some smart approach play that produced little reward apart from a Gower 30-yard effort that flew wide.
However three-goal top scorer Shaun Goater blew a great chance to double the advantage after 31 minutes. He met Gower's centre but saw his header hit the Oldham crossbar and the ball was then hacked to safety.
The missed chance spurred the Latics into action and they enjoyed their best spell of the half. Skipper Andy Liddell's corner was headed over by Rob Scott and then Killen's shot was saved by Flahavan.
Liddell then saw his shot from the right go narrowly wide before Southend increased their advantage. Lawson laid the ball off to Cole and his pinpoint cross found Gower at the far post, and his header gave Chris Day no chance in the Latics goal.
The heat took its toll in the second half as both sides settled in to a steady midfield battle that produced no shots on goals.
Oldham manager Ronnie Moore eventually decided to try to force the issue with a double substitution on 67 minutes and his shake-up was immediately rewarded.
The Latics pressured the Shrimpers 18-yard box and substitute striker Chris Porter laid the ball off to Richie Wellens, whose drive from the edge of the D gave Flahavan no chance.
The fresh legs helped the visitors maintain their pressure and they should have equalised on 75 minutes when 41-year-old sub David Eyres released Porter, who squared to Killen, but he scooped his shot over the bar.