When Kevin Davies headed in Matt Taylor's 43rd-minute free-kick things looked even worse for Hodgson, but a revitalised Fernando Torres volleyed home an equaliser before Joe Cole tapped in his first league goal for the club he joined in the summer.
It was Taylor's set-piece which allowed Kevin Davies to head home two minutes before the interval after Fabio Aurelio, making his first league start of the season, had fouled Rodrigo Moreno.
Liverpool could have been ahead by then as Maxi Rodriguez headed Dirk Kuyt's deep cross onto the top of the crossbar, while in injury time Lucas Leiva skewed wide.
The second half was only four minutes old when Steven Gerrard's first-time pass from David Ngog's knockdown picked out Torres on the penalty spot and he volleyed home his first goal since November 10.
Liverpool finished the game pressing for victory and they were rewarded with an injury-time winner. Gerrard's cross was touched back and substitute Cole tapped in from a couple of yards.