Stephen Hunt was a constant menace and Kevin Doyle twice had half chances which failed to test home keeper Chris Kirkland.
The second half began in similar fashion to the first with the Latics on top.
Sloppy defending from Reading gifted the ball to Brown whose fiercely struck 20-yard effort was tipped over by Marcus Hahnemann.
But for the second time in the game Reading settled as they desperately sought the win that would go a long way to securing their top-flight status.
Lita almost gave Steve Coppell's side the lead, but after doing brilliantly to skip past Emmerson Boyce on the left, his toe-poked effort drifted narrowly wide.
Duberry then almost bundled the ball home from close range following another corner.
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Coppell is satisfied with the draw
And with Reading bombing forward, a fine sweeping move saw Dave Kitson's goal-bound effort blocked by James Harper.
At the other end Brown's deflected shot forced a fine scrambling save from Hahnemann.
And Kitson reacted smartly to hack clear following a home corner.
But despite piling forward at every opportunity, neither side could force the winner.
Wigan are five points above the drop zone but still need two points to be certain of staying up while Reading are just one point and one place ahead of third-bottom with two games to play.
Wigan manager Steve Bruce:
"We started well but it petered out into two nervous, anxious teams fighting for their lives.
"For both sets of players the occasion and the magnitude made them forget how to play the game but who knows - that might be the point that keeps us in the league.
"We have got to go to Aston Villa next week and then Manchester United here but no one gave us a chance of getting anything at Chelsea so we will have to see what happens."
Reading boss Steve Coppell:
"I'm happy to have got a point and I would have taken that before kick-off.
"We didn't play for a point because we are not good enough to adjust our game to the circumstances.
"We do need to score, we have always been quite fluent in front of goal so we will work on that next week and try to get better."
Wigan:
Kirkland, Melchiot (Taylor 26), Boyce, Scharner, Kilbane, Valencia, Brown, Palacios, Koumas, Heskey (King 73), Bent (Sibierski 64).Subs Not Used: Pollitt, Skoko. Booked: Taylor, Kilbane.
Reading:
Hahnemann, Rosenior, Ingimarsson, Duberry, Shorey, Doyle (Little 69), Harper, Bikey, Hunt, Lita (Long 85), Kitson.
Subs Not Used: Federici, Cisse, Matejovsky.
Booked:
Shorey, Hunt, Bikey, Duberry.
Att:
19,043.
Ref:
Martin Atkinson (W Yorkshire).
BBC Sport Player Rater man of the match:
Wigan's Emile Heskey 7.25 (on 90 minutes).
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