Henry, who joined Wolves on-loan from Millwall at the start of the month, bundled home a Bakary Sako cross in the 50th minute as Oldham goalkeeper Mark Oxley let the ball slip from his grasp.
Leigh Griffiths then made the game safe from the edge of the area with a low drive in the 66th minute after being released by Sako.
The second-half double earned Wolves a ninth win in 11 league games and got their promotion push back on track after they dropped two points by conceding a late equaliser in their previous game against Coventry.
Lee Johnson's Oldham side had arrived at Molineux on the back of a three-match unbeaten run and after securing their first league success in seven games against Carlisle last weekend.
They more than held their own for long periods of the game but were frustrated in front of goal with substitute Johnson Clarke-Harris seeing his 57th-minute shot blocked and then Danny Philliskirk having a long range effort tipped over the bar by Carl Ikeme.