Fulham 1 Liverpool 2
Emile Heskey's crisp volley put Liverpool ahead on 17 minutes but Louis Saha's close range finish six minutes before the break levelled matters, only for Murphy's penalty to settle the tie before Luis Boa Morte was sent off.
Liverpool started lickety-split with Harry Kewell and Michael Owen ensuring the Fulham defence remained on the back foot although it was Sami Hyypia who was closest to opening the scoring in the early exchanges.
The towering Finn first had a smart header fumbled away by stand-in goalkeeper Mark Crossley and also glanced a corner across the face of goal, although in between he needed to be alert in defence to spare Jerzy Dudek's blushes.
Steed Malbranque's long ball caught Dudek in two minds and when the Pole slipped, Saha had a great chance to score but the Frenchman missed his shot and allowed Hyypia to nip in and clear the danger.
The visitors never allowed the pace to drop and got their reward on 17 minutes when Fulham old boy Steve Finnan's cross was stylishly volleyed beyond Crossley by Heskey.
With the tempo showing no signs of abating, even in the later stages of the half, Fulham hauled themselves on level terms in the 39th minute after a penetrating break from Moritz Volz.
The German surged down the right flank before Malbranque carried the threat into the penalty area. The schemer's attempted return to Volz was diverted across the six-yard box by Steven Gerrard and into the path of the unmarked Saha to finish from close range.
Saha could have grabbed his second goal four minutes after the interval when the ball broke his way on the edge of the area but his vicious volley was pushed away by a strong hand from Dudek.
It was end-to-end stuff at Loftus Road and Harry Kewell should have done better when Gerrard's pull back rolled his way but the Australian wastefully steered the ball over the bar.
Midway through the second half, The Reds - and Heskey - were agonisingly close to another goal when the England international's shot from an acute angle was deflected to safety by Jerome Bonnissel.
Despite the nip-and-tuck nature of the contest, the best chances fell to the visitors with Crossley forced to produce a superb save to deny Vladimir Smicer after Owen's deft header put the Czech Republic attacker through on goal.
With two minutes remaining, The Reds snatched the spoils after earning a penalty when Zat Knight was duped into fouling Florent Sinama-Pongolle. Murphy coolly dispatched the spot kick into the bottom corner to move Liverpool to within a point of Fulham.
The contest finished in a sour fashion when the temperamental Boa Morte was rightly sent off for a crude, high challenge on Sinama-Pongolle.
