His team-mates missed the focal point that the England striker provides as they enjoyed plenty of the ball, but Victor Moses and Raheem Sterling struggled to support lone striker Suarez.
After last weekend's 3-3 draw with Everton, today's result means Liverpool have conceded three or more goals in successive games for the first time since 1998. The Reds started the season with three successive clean sheets.
Hull's opener came as Moses ambitiously attempted to beat Ahmed Elmohamady in his own half and was dispossessed by the Egyptian.
As the visitors tried to readjust, Livermore neatly swapped passes with Meyler before his low shot turned from solid to unstoppable courtesy of a flick off the back of Skrtel's heels.
The visitors lacked the attacking edge of recent weeks, and Curtis Davies's foul on Jordan Henderson on the edge of the box seven minutes later immediately looked like their best chance of the match so far.
And so it proved as Gerrard swept the set-piece through a hole in the wall created by Skrtel and into the bottom corner.
A tame first-time strike from Suarez was the closest either side came to heading into the break ahead, although Yannick Sagbo's chasing and physicality unsettled the Liverpool backline on a couple of occasions.
As the visitors' passing game continued to break down in the attacking third, Hull grew into the second half with Davies's header going just wide before Skrtel was forced into a hurried clearance.
Philippe Coutinho's introduction, after he had been unable to train during the week with an ankle injury, jump-started a spluttering Liverpool attack.
But moments after Moses had seen a close-range effort bravely saved by Allan McGregor, the Reds' creaking defence folded again.
Kolo Toure and Skrtel got in each other's way attempting a routine clearance and Hull were hungrier in their pursuit of the loose ball, David Meyler holding off Glen Johnson to plant a composed finish into the bottom corner.
Liverpool's attempt to take at least a point yielded few clear openings and the nearest they came was another free-kick as Suarez had McGregor scrambling.
Instead, after Sagbo and Elmohamady had both squandered one-on-one chances, Liverpool were outnumbered for a third time and Skrtel's despairing attempt to block could only turn Tom Huddlestone's scooped shot into his own net.
It completed a miserable afternoon for both the Slovak defender and his team.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.