Four days after their FA Cup semi-final win over Tottenham, Pompey's dire situation was summed up as they made eight changes, with youngsters Matt Ritchie and Joel Ward handed debuts.
They were also only able to name four substitutes, but the Latics could not take advantage with Scharner and Scotland squandering a succession of chances.
Wigan had their first chance in the 13th minute when Charles N'Zogbia's cross was headed over by Scharner.
Latics midfielder James McCarthy then fired straight at Jamie Ashdown, but Pompey gave as good as they got and Tommy Smith's cross was headed over by Ritchie.
The debutant then wasted another decent headed chance at the far post before Scotland shot into the arms of Ashdown.
The ball was in the back of the net five minutes before the break but Scharner's effort was rightly disallowed for offside.
Austrian midfielder Scharner then wasted the chance of the half when he headed Maynor Figueroa's cross over from eight yards.
Pompey started the second half brightly with Smith heading over but it was all one-way traffic after that.
Scharner's night to forget got worse in the 55th minute when he blazed an N'Zogbia's cross over the bar, before he departed with Bolivian striker Marcelo Moreno coming off the bench.
Scotland then followed Scharner's lead by tamely heading wide on the hour as Roberto Martinez's men continued to pile forward.
With 15 minutes remaining the visitors were reduced to nine men momentarily when Anthony Vanden Borre and Papa Bouba Diop went off for treatment and they almost paid the price.
Moreno latched on to a long through ball but his shot at goal was saved by Ashdown.
Ritchie curled a free-kick over with 11 minutes remaining before being replaced by FA Cup hero Frederic Piquionne.
Five minutes from time McCarthy's shot was turned behind by Ashdown as Pompey held on to secure an unlikely point.