Portuguese midfielder Raul Meireles broke the deadlock just after half-time with a neat finish before £22.8million signing Luis Suarez became an instant hero with a second just over 20 minutes from time.
The Reds moved to within two points of sixth-placed Sunderland with their third win in a row as the Potters dropped to 11th with a second loss on the trot.
Stoke were taking it right up to Liverpool, especially through the midfield where they appeared to be outmuscling their opponents.
The first strong chance came in the 36th minute when Reds defender Glen Johnson was astonished to see his header from close range somehow kept out by a superb Asmir Begovic save before the Potters keeper again kept his side alive when he kept out Dirk Kuyt’s shot on the stroke of half-time.
GOAL But as play resumed and Liverpool were going to the Kop end, they were able to break the deadlock through Raul Meireles. Steven Gerrard’s free-kick was not properly cleared by the Stoke defence, with Meireles the recipient at the end to fire home with his left foot from close range for his third in four league games.
Stoke were desperate to get back into the contest although the home side were clearly up for a battle and were not about to surrender their lead with any ease.
GOAL The Uruguayan received a neat pass from Kuyt before rounding Begovic and knocking it home despite the best efforts of Andy Wilkinson who got the final touch but Suarez will surely claim a debut goal for his new club.
And that was enough to notch up another win for the Reds who moved closer to the top six as they get their season back on track.
Asmir Begovic (gk), Robert Huth, Abdoulaye Faye (Collins 65’), Andy Wilkinson, Danny Higginbotham, Marc Wilson (Fuller 67’), Jermaine Pennant, Salif Diao (Delap 61’), Dean Whitehead, John Carew, Jonathan Walters
Subs - Thomas Sorensen (gk), Rory Delap (61’), Danny Collins (65’), Ricardo Fuller (67’)