BRADFORD CITY forced 11 corners in the second half but were unable to conjure a winning goal and remain in the drop zone.
Bradford striker Billy Clarke made his second full debut as David Hopkin made two changes.
Clarke, after two substitute appearances since rejoining the Bantams from Charlton last month, came in for Hope Akpan to support from the left Eoin Doyle, who replaced George Miller.
Defender Kelvin Mellor was on the bench after recovering from a broken bone in his foot in October.
Plymouth manager Derek Adams named an unchanged side as the Pilgrims aimed to improve a record of five wins from seven games, which had lifted from the bottom of the league at the turn of the year up to 15th.
City players took the unusual step of going en masse to applaud fans in the Kop before returning to the dressing room ahead of kick-off.
There was a minute's applause before the game in tribute to former Bantams player Mick Kennedy and England's World Cup-winning goalkeeper Gordon Banks, who died this week.
Both sides lined up 4-2-3-1 and lone Pilgrims striker Freddie Ladapo soon turned in a shot from David Fox but was ruled offside.
Jack Payne hit over a first-timer from Lewis O'Brien's cutback but the first save came from Richard O'Donnell in the 21st minute as Anton Sarcevic hit a fine shot from Ruben Lameiras's deep corner.
Lewis O'Brien was the first in the book for a foul on Lameiras in the 27th minute.
Plymouth almost went ahead in the 42nd minute when they retrieved possession after a corner which had been cleared and Lameiras fed Graham Carey for a shot from the edge of the area which struck the base of O'Donnell's left-hand post.
However, it was goalless at the break.
David Ball blasted over into the Kop from the right after successfully chasing O'Donnell's long ball soon after the break. Balll then also struck the base of the far post in the 53rd minute after being set up by Jack payne's quick turn and feed.
City were cranking up the pressure and Payne fed the supporting Paul Caddis to hit a low drive which forced the first save of the game from Kyle Letheren in the 57th minute.
Ashley Smith-Brown went in the book for pulling back Clarke on halfway.
Ryan Taylor replaced Lameiras as Plymouth strengthened their attack before replacing Smith-Brown with Oscar Threlkeld.
Hope Akpan replaced Jacob Butterfield in the 80th minute as City made their first change.
City then went so close when Eoin Doyle's glancing header from Caddis's cross saw Letheren arching back to tip the ball away.
Jermaine Anderson for Payne was City's second change as time began to run out.Caddis was again the provider only to see Akpan to blaze over unmarked from 10 yards.
Anderson was the next to go close with a smart back-heel from Doyle's driven cross but Letheren kept it out at his near post.
Miller replaced Doyle in the 90th minute ahead of three minutes of stoppage time.
Nial Canavan then slid in to clear after Ball attempted to knock the ball across for Anderson to tap home following a crossfield ball from O'Brien and the game ended in stalemate.