Oldham were in almost total command in the first half but Hammond pegged them back on 61 minutes as the visitors showed fighting spirit.
Oldham were hit by injury and suspension, with 13-goal top scorer Chris Porter and midfield playmaker Richie Wellens both forced to sit out the match.
They still played well for 45 minutes and missed a number of chances after Paul Warne gave them the lead, but Brighton showed why they had won ten of their previous 13 games.
Oldham winger Chris Taylor set up Warne for an early chance which he headed straight at the keeper but Warne soon made amends with a breakthrough in the 18th minute.
He controlled Andy Liddell's pass 12 yards out with his back to goal and turned sharply before firing into the bottom corner.
Young striker Chris Hall, who was replacing Porter in the Oldham line-up, sent the next opening too close to Wayne Henderson and also headed at the keeper from a corner.
Little was seen from the Brighton forward suntil Alex Revell found space at the near post and tested Les Pogliacomi in the Oldham goal.
Taylor was denied by the woodwork before half-time as he dashed from the centre circle into Brighton's penalty area and was frustrated when his low shot rebounded off the post.
But Brighton showed they were not beaten as Dean Bowditch headed off target and Jake Robinson had a goal disallowed for offside at the start of the second half.
Their equaliser came after Bowditch delivered a deep free-kick from near the touchline and Oldham were unable to clear it.
Hammond seized on the loose ball and lashed his angled volley beyond Pogliacomi from eight yards.
Brighton took over the game and almost made it 2-1 through lively substitute Joe Gatting.
But Oldham went closest to a winner as midfielder Gary McDonald somehow hit both the crossbar and the post with the same header before substitute Matthew Wolfenden headed over in the dying seconds.