Romain Padovani and Wes Fogden put in impressive displays in the centre of the park as lowly Pompey frustrated the leaders.
In fact Portsmouth could have stolen all three points but for a fine save by Spireites keeper Tommy Lee from Fogden.
Barker said: "We sat down and gave them a really specific job to do - and I must say I thought they were fantastic.
"Wes' energy is just so contagious. He covers so much ground, but so does Romain and he was a real goal threat in the first half.
"That was important because Jake Jervis could have become isolated up front on his own.
"But I thought the two advanced midfield lads - and Toumani Diagouraga just behind them as well - were excellent."