Harry Redknapp's side were looking for a fifth straight win but wasted a string of chances to secure it, with Charlie Austin the main culprit.
The R's had won their previous four matches 1-0 but could not even muster the solitary goal which would surely have seen off a Brighton side who are hardly prolific themselves.
With Bobby Zamora and Andy Johnson sidelined it was left to Austin to shoulder the goalscoring burden.
And the fact Rangers ended the night with Armand Traore joining the attack showed why Redknapp wants to bring in another striker on loan.
The hosts did had the ball in the net after only eight minutes, but Shaun Wright-Phillips was a long way offside when he played the ball across the face of goal for Joey Barton to tap in.
Moments later Gordon Greer's dreadful pass along the edge of the area almost let in Gary O'Neil but Matt Upson managed to clear the danger.
Rangers lost defender Nedum Onuoha to injury midway through the first half, paving the way for Benoit Assou-Ekotto to make his debut from the bench.
The Tottenham loanee almost made an instant impact when he overlapped and crossed for Austin, but although the striker turned smartly, he could not hit the target.
Winger Matt Phillips, making his full Rangers debut, was next to try his luck but his angled drive flew narrowly over.
Then came two chances in a minute for Austin, who was mightily relieved to see an offside flag after somehow dragging the first one wide from all of three yards out.
Moments later he met Barton's corner with a firm header but planted it straight at Tomasz Kusczcack.
Brighton showed little ambition in the first half, with a couple of long-range efforts from Keith Andrews the closest they came.
It was more of the same after the interval with Barton forcing a fine save from Kusczcack from one curling free-kick and seeing another bounce inches wide after taking a deflection which left the Seagulls keeper stranded.
Kuszczak was beaten when Phillips nodded the ball over him during an almighty goalmouth scramble but Greer was on hand to hack the ball off the line.
Their final chance came on the stroke of full-time when Richard Dunne headed Barton's free-kick over and Brighton escaped with a point.