And, even though inspirational captain Steven Gerrard was back for the Reds, they again flattered to deceive with Wolves keeper Marcus Hahnemann hardly called into any serious action.
Riera flashed a header across the Wolves goal as he could not to get enough purchase on his effort in order to send it goalwards, and the urgency with which Liverpool started the game quickly evaporated.
Instead, the home side quickly got into their stride after a sluggish start and, as they comfortably held the Reds at arm's length, they almost took the lead.
A counter-attack saw left winger Matt Jarvis outpace Jamie Carragher and get in a low cross to the near post and, even though Doyle got to it first, his effort was deflected wide off Insua.
Benitez defends team selection
The threatening Jarvis was his side's best attacking outlet and he drifted a cross to the far post, where Kevin Foley sent a header straight at keeper Pepe Reina from a tight angle.
Wolves have only scored 17 goals in 21 league games this season - the lowest in the Premier League for the present campaign - while Liverpool have struggled for away goals with 17 in as many games away from home in all competitions.
Liverpool's problems at Molineux were as a result of a lack of invention as Gerrard and left-winger Riera lacked match sharpness, along with right winger Maxi Rodriguez, who was making his full Reds debut.
We have turned the corner - Gerrard
Riera did again go close when his mistimed volley almost looped under the crossbar before the alert Hahnemann saved.
The impressive workrate and 4-5-1 formation of Wolves also had plenty to do with them keeping Liverpool at bay, with the tough midfield tackling of Karl Henry and harrying of lone frontman Doyle a feature of the home side's play.
As the game progressed, Wolves grew in confidence and Doyle sent a well-struck shot over.
Liverpool's attacking midfielder Alberto Aquilani had to watch from the touchline as the visitors continued to be repelled by Wolves and had to settle for a draw.
Liverpool are now fifth and three points behind Tottenham but sixth-placed Manchester City are level with the Reds with two games in hand, while Wolves are fourth from bottom courtesy of a better goal difference than Burnley.
Liverpool boss Rafael Benitez: "If you analyse the game, it was a fair result. In the first half, we were in control, although we didn't create chances. The final pass in the final third was the difference.
"In the second half, they pushed harder. We still had some good counter-attacks but again the final pass was the difference. It was a fair result."
Wolves manager Mick McCarthy on striker striker Kevin Doyle: "If you see a better performance from a centre-forward than Doyle showed, I would like to see it. If he had just managed a goal, it would have been one of the best all-round performances.
"He is physically strong enough to play that role. We changed the system and I don't think our keeper had a save to make. I don't think we were troubled.
"It was a really solid performance and it's great to get off 19 points because we've been there for too long."
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