Saddlers boss Paul Merson was left frustrated once again as his hit and miss team only came to life when the points had already got away from them.
Porter scored his eighth goal since moving to Oldham from Bury during the summer in a £100,000 transfer.
And Warne, who arrived on a free from Rotherham United, took his own tally to seven.
Porter could have given Oldham the lead on 25 minutes when he got on the end of Richie Wellens' free-kick and lifted his shot over the bar.
Big defender Guy Branston was also off target with a good chance before Oldham broke the deadlock after 34 minutes.
Warne's cross from the left found Porter getting away from his marker six yards out and he thumped the header underneath Joe Murphy's bar.
Murphy then saved Andy Liddell's free-kick as Oldham began to take over.
Warne blazed wide after an hour, while Richard Butcher saw his long-range shot unluckily hit a defender and go out for a corner.
But the Latics doubled their lead when Paul Edwards crossed to the far post and Warne headed back across the keeper from eight yards.
Walsall replied just 60 seconds later when substitute Kris Taylor shot from the edge of the box and his effort went through a packed defence before finding the bottom corner.
Both keepers were busy in the last five minutes as Murphy denied Liddell and Chris Day made a fine save from Daryl Taylor.