The 46-year-old has been granted what amounts to a four-game interview to impress after the sacking of Simon Grayson 10 days ago and, after winning at Bristol City last weekend, looked to have remained unbeaten on Saturday when Luciano Becchio cancelled out Craig Mackail-Smith's opener.
But, just as four minutes of injury time were displayed, Liam Bridcutt won the ball in midfield and played in Navarro and his low drive from the edge of the box went in via a deflection off Adam Smith to silence Elland Road and keep the Seagulls unbeaten in 2012.
It was unfortunate for Redfearn and his players who had done enough to at least warrant a point but, once the final whistle was blown, the anger from the terraces - which had prompted a pre-match protest march against chairman Ken Bates - returned, with several fans voicing their disapproval at Redfearn's temporary appointment.
The former Barnsley midfielder was the first man since Grayson to occupy the home dugout since December 2008 - a home defeat under Gary McAllister - and his side set off as though a loss was not an option today.
They should have been ahead inside four minutes - Becchio's header grazing the post after Robert Snodgrass has turned inside Joe Mattock - and had a seemingly solid shout for a penalty turned down not long after.
Smith's cross from the right fell to Ross McCormack and, as the 15-goal striker teed up a shot, he was clattered to the ground by Adam El-Abd. Referee Graham Salisbury did not agree with the protests of the Leeds players, though, leaving Redfearn to open a heated conversation with the fourth official.
McCormack, a scorer of two goals when these sides drew 3-3 in September, then shot over from an ambitious 35 yards before former Leeds loanee Sam Vokes, now on a temporary deal with Brighton, played in Navarro whose effort was also too high.
That effort signalled the start of some Brighton pressure, with Navarro and then Bridcutt working Andy Lonergan from distance, with Leeds responding through a near-post drive from Smith that nearly caught Peter Brezovan napping in the away goal.
Neither side was particularly able to get in behind the other during the opening half, but that changed within 60 seconds of the restart and only some desperate defending from Mattock kept Brighton level.
Aidan White's pass put Snodgrass into the area and, after his low cross was shelled by Brezovan, Mattock prevented Becchio from bundling in at the back post.
If that was the game's closest shave it was quickly bettered, with Lonergan producing a fine one-handed save to keep out Ashley Barnes, although the Leeds captain nearly undid his good work with two fumbles from corners - the second of which saw him eventually fall gratefully onto a Vokes header.
With both sides now fully committed to attacking, Snodgrass worked some space for Smith whose edge-of-the-area scoop floated over, before McCormack was also off target after Adam Clayton's outside-of-the-boot ball from deep in his own half had cut Brighton open.
But, having made the majority of the running, the home side would fall behind with 13 minutes remaining, with Mackail-Smith doing the damage just three minutes after replacing Vokes.
The Leeds defence lost the Scotland international in the box and, once Vicente's cross had picked him out, his eighth goal of the season duly followed.
However, their lead would last no longer than two minutes, with Becchio peeling off his marker at the front post and glancing a Snodgrass corner into the far corner.
But there was still more drama to come, with Bridcutt winning the ball and giving Navarro the chance to seal victory - an opportunity he duly took.