Nigerian striker Yakubu Ayegbeni's sixth goal in seven games ten minutes from time was enough to earn them the draw they needed to leave them certain of staying up, barring some freak results between now and the end of the season.
Yakubu had been in scintillating form over the last six weeks alongside new strike partner Lomana LuaLua and he was in the right place at the right time to lash the ball home from close range after goalkeeper Edwin Van der Sar had failed to gather full-back Matt Taylor's cross from the right.
Van der Sar almost cost his side a goal in only the seventh minute of a poor first half when he failed to hold a hopeful long ball from Nigel Quashie, but team-mate Alain Goma was on hand to save his blushes and clear with LuaLua closing fast on the edge of the area.
But Portsmouth should have found themselves in front nine minutes later when Yakubu wasted the best chance of the opening 45 minutes when unmarked just eight yards out.
LuaLua was the architect as he burst down the right before crossing invitingly, but the Nigerian could only head over with the goal at his mercy and Van der Sar stranded.
Redknapp was forced into an early change on 22 minutes when right-back Linvoy Primus limped off with a hamstring problem and was replaced by teenager Richard Duffy, who was making his Premiership debut, but the change did little to halt the home side's momentum and they went close again nine minutes before the interval.
LuaLua again found room on the right and attempted to cross but his centre sliced off his foot and almost caught Van der Sar out at his near post, but the ball rebounded off the upright to safety.
Fulham came out fired up immediately after the interval and were unlucky not to be in front within 20 seconds of the restart through Davis.
Steed Malbranque and Junichi Inamoto combined to set the midfielder up to unleash a thumping 20-yard drive which flew past goalkeeper Shaka Hislop only to hit the woodwork.
Davis' midfield colleagues Sylvain Legwinski and Inamoto also went close from 12 yards out, but Van der Sar gifted Pompey the lead when the ball squirmed under his body to fall invitingly at Yakubu's feet.
Fulham threw players forward in search of at least a point after falling behind and they earned a deserved draw when substitute Brian McBride produced a clinical finish with six minutes remaining.
McBride, who had only been on the pitch seven minutes, was allowed time and space by Portsmouth defence to give Hislop no chance with a low left-foot shot from the edge of the area.