The result moves Common up to third in Sussex County Football League Division Two - above Eastbourne United AFC on goal difference - and both clubs will play their final games of the season on Saturday.
Third-bottom Oakwood opened the scoring with virtually the last kick of the first half. Common failed to clear a right wing corner and Alfred Hammond hit a bouncing shot into the bottom corner.
Both sides had their moments prior to that, although Oakwood had squandered the two best chances. Common goalkeeper Jon Saunders made a fine double save from the first of them and the other was blazed over the crossbar.
Common cranked up the pressure in the second half and after Adam Smith had struck the crossbar from just outside the six yard box, Lewis Hole played in substitute Chris Cumming-Bart for a 75th minute equaliser. Common had a chance to win it late on, but Steve Morris headed wide from a Russell Eldridge corner.
Elsewhere tonight, Rye United moved up to fourth in Sussex Division One courtesy of a superb 6-2 victory away to Hailsham Town which extended their fine run to one defeat in 17 games.
Rye surged into a four-goal lead after 35 minutes and were 5-1 up at half time thanks to a brace of goals each from Olly Lockyer and Matt Maclean, and one from Sam Crabb. Sam Cooper rounded-off the scoring late on.
Westfield moved level on points with fifth-placed Broadbridge Heath in Division Two via a 2-1 win away to bottom club Saltdean United. Goals from Mike Booth and Steve Thomson swung the match Westfield’s way after they fell behind early on, and a point from their last game on Saturday will ensure a top five position.
See Friday’s Observers for full reports.
Sussex Division One top five (played-points): 1 Peacehaven & Telscombe 40-93, 2 Redhill 40-87, 3 East Preston 39-82, 4 RYE UNITED 40-80, 5 Pagham 41-80.
Sussex Division Two top six (played-points): 1 Littlehampton Town 33-82, 2 Newhaven 33-70, 3 LITTLE COMMON 33-65, 4 Eastbourne United AFC 33-65, 5 Broadbridge Heath 34-55, 6 WESTFIELD 33-55.