Southampton 3 - Fulham 3
Redknapp, who has been in charge for six games, saw his side come from behind twice to earn a point against a Fulham side who dominated throughout the second half.
The visitors made a promising start with Senegalese star Papa Bouba Diop in the centre of the action.
On 17 minutes Diop almost put through his own net when he sliced the ball over the crossbar following a Danny Higginbotham left-wing cross
But the midfielder went up the other end and gave Fulham the lead when he outjumped Claus Lundekvam to head in Mark Pembridge's precise free-kick from the right.
But Southampton fought back and scored twice in eight minutes to turn the game on its head with a double from striker Kevin Phillips.
Just seconds after Diop's opener Phillips got in on the act to head in Fabrice Fernandes' centre to level matters.
And on 29 minutes Phillips exchanged passes with strike partner Peter Crouch before turning defender Zat Knight to curl in his seventh goal of the season.
But just two minutes before the interval Fulham clawed their way back level when Steed Malbranque was quickest to react in the penalty box.
Luis Boa Morte cut in from the left and saw his angled shot well saved by Antti Niemi, but Malbranque was on hand to tap in the rebound from eight yards.
The visitors started the second half as they had the first and got themselves in front again after good work by Pembridge.
The former Welsh international's throughball played in Tomasz Radzinski and he made no mistake with a right-foot shot from ten yards.
Canadian international Radzinski was involved three minutes later when Fulham should have extended their lead.
After good work from the byline, Radzinski centred to Andy Cole who shot well wide when well placed.
The influential Pembridge continued to create chances for the visitors and on 63 minutes another precise pass played in Cole, whose right-foot shot was turned round the post by Niemi.
And from the resulting corner, again taken by Pembridge, substitute Collins John saw his header sail inches over the crossbar.
Another Pembridge set-piece caused havoc with 20 minutes remaining when this time defender Knight saw his shot from three yards somehow kept out by Finnish international Niemi.
And Fulham were made to pay for their missed chances when Southampton again levelled on 71 minutes.
Swede Anders Svensson found space down the right and his low cross was turned into his own net by Liam Rosenior, leaving Fulham keeper Edwin Van der Sar stranded.
Southampton felt aggrieved that they didn't have the chance to snatch victory late on when defender Knight seemed to handle in the box, but referee Graham Poll turned away the home side's protests.