The Uruguayan slotted home the Reds' second goal of Wednesday's game in front of the Kop to ensure Fernando Torres' £50million move to Chelsea was no longer the major talking point.
And if questions were being asked about how the Reds would cope in their former striker's absence, then efforts by Suarez and Portugal midfielder Raul Meireles - with his third goal in four matches - provided a swift answer at Anfield.
Record £35million signing Andy Carroll's introduction to the crowd before kick-off was the closest he is likely to get to the pitch for a month as he recovers from a thigh injury.
Unfortunately for Liverpool this was exactly the sort of game from which they would have benefited from the 6ft 3in powerhouse striker.
Conversely, it did not seem that suited his fellow new arrival, although arriving as a second-half substitute with his side already ahead made the task much easier.
The ball spent much of the first half in the air, which benefited Stoke far more than it did their hosts, and as a result Dirk Kuyt found his role as lone frontman a frustrating one at times.
Saying that, he had at least three chances of which at least one would probably have been converted by Torres.
Manager Kenny Dalglish had tailored Liverpool's formation specifically for the Potters, lining up 3-4-2-1 with Lucas Leiva and Fabio Aurelio holding in midfield and Steven Gerrard and Meireles supporting the Holland international up front.
The first chance fell to Sotirios Kyrgiakos, returning to the team in that back three to combat the aerial threat of John Carew, as he headed Gerrard's corner goalwards only for former Liverpool midfielder Salif Diao to clear two yards out.
Jon Walters fired over an angled shot from 10 yards and Carew headed over another ex-Red Jermaine Pennant's right-wing cross, with the hosts having penalty claims turned down when the ball appeared to hit Robert Huth's hand.
Stoke's tactics of keeping everything compact squeezed the life out of Liverpool and disrupted their passing game.
Suarez's appearance off the bench to jog down the touchline brought a standing ovation from the Kop, who as a result almost missed Asmir Begovic's brilliant reaction save to keep out Glen Johnson's close-range header.
Kuyt nodded wide Gerrard's cross and volleyed over from close range before shooting straight at the Stoke goalkeeper when a rare passing move involving Brazilians Lucas and Aurelio cut open the defence.
Within two minutes of the second half resuming Diao was booked for bringing down the advancing Daniel Agger and from the resulting free-kick Liverpool, somewhat fortuitously, took the lead.
Gerrard's low, driven free-kick deflected off Marc Wilson on the end of the wall to Kyrgiakos 12 yards out and although Huth nicked the ball off the defender Meireles was on hand to smash home left-footed.
Carew almost snatched an equaliser on the counter-attack with a shot which flashed across goalkeeper Jose Reina and wide of the far post before, just after the hour Suarez got his chance to start repaying his £22.8million transfer fee - a club record for a few hours on Monday.
His first contribution was to engage Abdoulaye Faye in a sprint which resulted in the Stoke centre-back pulling a hamstring.
One clever backheel to set up Martin Skrtel showed the Uruguayan was not short of confidence, despite not playing a game since December 8 because of a seven-match suspension for biting an opponent while playing for Ajax.
His next involvement was more decisive and was what the Kop had been waiting for.
Kuyt's through-ball sent the forward racing through and having gone round Begovic he rolled the ball goalwards.
For a few seconds it appeared Wilkinson would cut out the shot but his desperate clearance came back off the post and bounced over the line.
While the crowd were still celebrating, Reina ensured there was no frantic final few minutes by punching away Walters' shot.