The Clarets have now conceded just nine goals in 30 Championship matches this season, yet Matt Ritchie twice went close to breaking through their impressive defence.
At the other end, the impressive Andre Dozzell cleared of the line late on from Lucas Pires, but otherwise, the hosts admirably stood firm.
And here are our player ratings...
1. Portsmouth midfielder Matt Ritchie (30) shoots during the EFL Sky Bet Championship match between Portsmouth and Burnley at Fratton Park, Portsmouth, England on 1 February 2025.
Matt Ritchie fires in a shot in Pompey's goalless draw with Burnley. Picture: Jason Brown/ProSportsImages Photo: Jason Brown
2. Nicolas Schmid - 7
Good saves from Foster and Anthony within a couple of first-half minutes, but otherwise had very little to do thanks to the defensive performance in front of him. Photo: Jason Brown
3. Zak Swanson - 7
(Replaced by Terry Devlin on 87 mins) Has become a player Pompey can really rely on and the right-back produced another solid defensive display. As ever, always gives an attacking outlet. Photo: Jason Brown
4. Conor Shaughnessy - 8
(Replaced by Hayden Matthews on 71 mins) Handed his first start since August and, as expected, made a huge difference. Such a classy player and it was as if he had never been away. Partnership with Atkinson will be crucial to staying up. . Photo: Jason Brown