Leicester preserved their year-long unbeaten home record with a narrow victory over a gutsy Worcester.
Willie Walker put Worcester ahead with a penalty, but two kicks from Jeremy Staunton reversed the advantage.
Moody bundled over for a converted try to put Leicester in charge but again Walker's boot kept Worcester in touch.
Tom Wood gave Worcester hope of a shock when he crossed for a try but Walker missed the conversion and Staunton made him pay with a drop goal and penalty.
Worcester forced the Tigers to twice come from behind to clinch their third win of the season.
Missing 10 players through injury, the hosts lacked cohesion and the game was also affected by strong winds which caused problems for the kickers.
Worcester worked tirelessly in defence but lacked the cutting edge to cause an upset, although they did take the lead after barely a minute.
Leicester were penalised for killing the ball in a ruck after just 23 seconds, and Walker banged over the first of his three first-half penalties.
Staunton missed with an 11th-minute penalty attempt, and was also wide of the target with a drop goal effort four minutes later, but Worcester had already been penalised at the breakdown and he landed the penalty.
A second penalty from Staunton after Worcester infringed under mounting pressure put Leicester ahead, but Walker levelled with a well-struck penalty after winger Miles Benjamin managed to break into Tigers' territory.
It proved a brief respite for Worcester as Ryan Powell was forced to nudge the ball into touch close to his own line.
Leicester won the resulting line-out and Moody emerged from a pile of bodies to claim the try. Staunton added a difficult conversion from the right-hand touchline.
His effort was eclipsed by Walker who closed the half with a wind-assisted penalty from five metres inside his own half that bounced over off the crossbar.
Worcester brought on prop Matt Mullan, hooker Aleki Lutui and lock Graham Kitchener after the break, and they went ahead again when a sustained attack created the overlap for Wood to gallop over.
Walker was unable to add a difficult conversion into the wind, and Leicester were back in front within three minutes when Staunton slotted a drop goal.
He hooked a penalty chance wide a minute later, but made no mistake when Worcester then took down a scrum, his third penalty proving the final score of a lacklustre contest.
Leicester head coach Richard Cockerill: "I found it frustrating how the game was refereed (by Chris White).
"Worcester gave away 15 penalties, the majority of them in their own half, and it starts to become frustrating for the team that wants to play.
"How many times do they have to infringe before there is a warning? There were no warnings in the first half and that is a frustration.
"They came here to try and spoil us and grind out a win."
Worcester director of rugby Mike Ruddock:
"I thought Chris White was excellent and refereed the game superbly. It was great to see someone of his quality out there.
"There were some injuries in the Leicester team and it was probably a day when we could have got a result here.
"There's plenty of spirit in this team, it's a case of being more consistent and accurate week-in and week-out.
"We will keep working to improve, and hopefully we will become an even better side and the near-misses we have had in this first phase will be transferred into some big wins."
Leicester: Hamilton; J Murphy, Hipkiss, Allen, Smith; Staunton, Grindal; Stankovich, Duffy, Castrogiovanni, L Deacon, Kay, Croft, Moody, Crane. Replacements: Amorosino for Smith (42), Ayerza for Stankovich (53), Davies for Duffy (58), White for Castrogiovanni (58). Not Used: Parling, Newby, Youngs, Twelvetrees.
Worcester: Latham; Gear, Grove, Tuitupou, Benjamin; Walker, Powell; A Black, Fortey, Taumoepeau, Rawlinson, Gillies, Wood, Sanderson, Talei. Replacements: Arr for Powell (73), Lutui for A. Black (51), Mullan for Fortey (51), Kitchener for Gillies (51). Not Used: Ruwers, Cox, Carlisle, Rasmussen.
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