A run of good form means that Pompey are now sitting just three points off the League One summit.
They brought their fine away form back to Fratton Park with a comfortable victory over Crewe at the weekend.
Now there is another south coast contest this evening, with 19th-placed Oxford the latest opponents.
And Kenny Jackett knows there is still plenty of work to be done this season if his side are to achieve their ultimate goal.
The Blues boss said: “We want to improve our home record and made a good stab of doing that on Saturday.
“All of the focus has been on not dwelling on that result, however, and looking forward because the next game comes at your pretty quickly.
“We’ll have to make sure that we’re concentrating on the challenge ahead and doing our best to enjoy our football.
"We want to be up there challenging among the other top teams, so we’ll need to be consistent and play to our maximum."
“Oxford had a good win at the weekend and will be looking to climb the table – which they’re certainly capable of.
“The league is starting to sort itself out now, but I would suggest that they are in a bit of a false position.
“We obviously played them very recently in the play-offs and there have been some changes in both sides, but not many.
“They were both close, hard-fought and competitive games between two good sides, but this is a fresh season.
“We want to be up there challenging among the other top teams, so we’ll need to be consistent and play to our maximum.”
Pompey will still be without midfielder Michael Jacobs, who has now been missing for a month with a knee injury.
Jackett said: “He is going well in terms of his rehabilitation from what was a bad tackle at Sunderland and will probably be out for another two weeks.
“Ryan Williams is the only other one who’s been injured and he’ll have a fitness test to see whether he’s available.”