England discard Toby Flood landed five kicks for an individual 13-point haul as Leicester denied battling Worcester a first Premiership win of the season.
The bottom side put in their best performance of the campaign against the reigning champions.
But they were beaten by two tries by wing Niki Goneva, both converted by Flood, who kicked three penalties.
Josh Drauniniu scored Worcester's try, converted by Chris Pennell, who also landed four penalties.
Worcester's losing bonus point for the narrowest of their 13 straight league defeats under Dean Ryan was only their fourth bonus point of the season.
Nonetheless, despite such a spirited display against a Tigers side weakened by injuries and international calls, Worcester have now lost 18 successive Premiership games since 1 March last year.
Urgently needing a good start against the reigning champions, Worcester could not have got off to a worse one.
Inside five minutes, Goneva had shown good anticipation to pick off Warwick's long pass close to the halfway line and, having safely collected the ball in the bread basket, he raced away to go under the posts, with Flood converting.
Worcester responded well when Leicester then erred three times in five minutes and Pennell slotted all three penalties to earn the Warriors a 9-7 lead.
Blaine Scully's burst then opened the door for his fellow winger Goneva to race in down the left touchline for the Tigers top scorer's eighth try of the Premiership campaign.
Flood again converted for a 14-9 lead, a five-point half-time lead that Leicester still held when Pennell's fourth penalty was answered by a first from Flood.
It might have been even closer had Pennell not hit the post with a long-range penalty right on the stroke of half-time.
But Flood then matched that with his only missed kick of the night five minutes into the second half.
And Worcester looked to have cashed in when Drauniniu went in at the right corner five minutes later, Pennell converting from the touchline to give his side the lead for the second time.
Flood's boot quickly restored Leicester's lead before Pennell kicked Worcester back in front on 67 minutes.
But Flood had the final word nine minutes from time, keeping his nerve wide out on the right from 45 metres.
VIEW FROM THE DRESSING ROOM
Tigers coach Richard Cockerill told BBC Radio Leicester:
"That's the best Worcester have played this season and you have to give them credit. They ran hard and put us under pressure.
"They've had some disappointing results this season, but they have some good players and it had to turn for them at some stage.
"We're just thankful to have won in the end, as conditions were tough. We created opportunities and should have taken them."
Warriors coach Dean Ryan told BBC Hereford & Worcester:
"It was a huge performance. Let's see if we can replicate it. We showed raw courage and passion.
"We got one point. We need to go out next week and look to get more points.
"We're learning how to be a team. We're trying to build a team that cares.
"Bad start, but we didn't let it get it us. The way we reacted was good."
Worcester: Pennell; Drauniniu, Grove, Fatiaki, Lemi; Warwick, Arr; Fainga'anuku, Creevy, Andress; Percival, Galarza; Williams, Betty, Thomas (capt).
Replacements: Senatore for Williams (49). Shervington for Creevy (58), O'Donnell for Andress (63).
Not Used: Porter, Schofield, Hodgson, Mieres, Matavesi.
Leicester: Tait; Scully, Smith, Allen, Goneva; Flood (capt), Youngs; Ayerza, Hawkins, Mulipola; Deacon, Slater; Gibson, Salvi, Waldrom.
Replacements: Balmain for Mulipola (63), Mafi for Youngs (64), Mele for Gibson (64), Hamilton for Goneva (77).
Not Used: Thacker, Stankovich, Matera, O Williams.
Referee: Andrew Small (RFU).