A Daniel Agger header was enough to return Liverpool to winning ways as Southampton were dispatched 1-0 at Anfield.
On a day when Lucas Leiva returned from three months on the sidelines, the Reds were worthy winners.
They twice hit the woodwork before Agger found the net, and could have had a penalty when Suarez was dragged back in the box.
The Reds controlled the first half but had to bide their time for an opener. It almost came through Glen Johnson on 10 minutes when he met a Luis Suarez cross at the near post, but the resulting shot spun across goal and wide.
Jonjo Shelvey, playing in an advanced role alongside Suarez and Raheem Sterling, was twice denied in the opening period - once by a Paulo Gazzaniga save and again when an angled smack clattered the inside of the post.
There was a decent penalty shout when Suarez was dragged back inside the box, but he still managed to get a shot in, while Skrtel mis-controlled a Steven Gerrard centre with the goal at his mercy.
The opener finally arrived on 42 minutes when Suarez hit the crossbar with a bending free-kick. The ball fell to Johnson in a wide position and his cross was headed into the top corner by Agger.
Southampton gave a good account of themselves in the second period, allowing Lucas to come into his own defensively, holding the midfield with a composure and strength that Liverpool have missed over the previous months. The Brazilian lasted 88 minutes before being replaced by Jamie Carragher.
Jose Enrique could have put the game to bed when he burst into the box to receive a Suarez flick, but the Spaniard's aim was off. He again found himself in the box with 15 minutes remaining, this time forcing a palmed save with a well executed half-volley.
An intricate sequence of passing involving Johnson, Gerrard and Sterling gave Suarez a chance from close range, but he did not have time to adjust and the opportunity went begging.
The final chance of the game fell to Suarez, who dragged wide from 10 yards.
Liverpoolfc.com journalists' man of the match: Steven Gerrard