Proceedings got off to a slow start as both sides took a patient build-up in the opening 15 minutes.
Bucs then stepped up a gear as Dove Wome was played through behind the Celtic defence but the Togolese attacker failed to beat Patrick Tignyemb in a one-on-one.
Celtic were unfortunate not to open the scoring around the 20-minute mark as Musa Nyatama's header rattled the woodwork.
The visitors had another opportunity just before the break as Wome again broke away from his marker but blasted his effort wide of the target with only Tignyemb to beat.
Pirates retained the momentum into the second half, with Mpho Makola, Wome and Tendai Ndoro central to their attacking threat but the Celtic defense held firm.
Makola should have done better with his opportunity in the 73rd minute as he picked up a great pass from Abbubakar Mobara, but hurried his effort and missed the target.
Five minutes later, substitute Thamsanqa Gabuza got onto the end of Makola's corner kicke but could only direct his header towards Tignyemb, who was well positioned.
In the fying minutes, Makola had an opportunity with a free-kick outside the Celtic area, but Tignyemb was once again up to the task as he palmed the ball to safety.
The match ended scoreless with Bucs failing to move up into to the top half of the table, while Celtic are all but safe from relegation as they sit three points above 15th-placed Baroka.