Sitting outside the top six on goal difference at the start of play, the Clarets remain in eighth place but are now two points adrift with two games to play.
David Nugent opened the scoring against his former club with a superb drive into the top corner, but Chris Eagles pulled out an equally good effort to equalise.
It was Graham Alexander day at Turf Moor, with the veteran defender given a guard of honour by both teams before being presented with a special award before kick-off to mark his 1,000th career appearance.
He was on the bench as Burnley manager Eddie Howe named an unchanged line-up as his side looked to make it four straight wins.
Nwankwo Kanu and David Cotterill came in for Dave Kitson and Carl Dickinson as Pompey made two changes from the side which drew 0-0 with Swansea on Saturday.
Boss Steve Cotterill could again only name four subsitutes.
The visitors started brightly but it was the Clarets who had the first chances of the game.
Jay Rodriguez sent a header over the crossbar and Eagles was not too far away with a 25-yard drive shortly afterwards.
Wade Elliott headed straight into the arms of Jamie Ashdown from a Michael Duff cross in the 20th minute as Burnley began to dominate.
Ashdown was forced into a double save in the 29th minute, parrying Chris McCann's 20-yard shot straight to Fox whose cross-shot was fumbled by the keeper but grasped at the second attempt.
Portsmouth finally responded with their first opening of the game after 35 minutes.
Cotterill whipped in a dangerous cross for Nugent, but the striker's close-range header was gathered by Brian Jensen.
And they were enjoying a decent spell of pressure as half-time approached, although Burnley had strong claims for a penalty waved away in injury time after the ball looked to strike the arm of Joel Ward.
The home side started the second half on the front foot with Chris Iwelumo heading over from Elliott's teasing cross, while at the other end Jensen easily dealt with a long-range strike from Greg Halford.
Pompey snatched the lead in the 57th minute when Kanu rolled the ball to Nugent 20 yards out and he crashed an unstoppable shot into the top corner.
Burnley hit back straight from the kick off, missing two gilt-edged chances in a minute.
Elliott found himself clean through but his weak attempt was saved by Ashdown, then Iwelumo sent a header straight at the keeper from six yards.
Howe threw on Nathan Delfouneso and Steven Thompson in a bid to rescue something from the game, and the Clarets levelled in the 74th minute.
Tyrone Mears played the ball to Eagles on the right-hand corner of the area and he produced a superb finish to equalise.
Burnley pushed for a winner and almost got it when Delfouneso found some space and cracked a shot from close range which Ashdown did well to parry.
But it was Portsmouth who almost snatched the points at the death as Nugent found himself one-on-one with Jensen but the keeper came out on top.