Robinson saw the Tigers go behind to a penalty from the Warriors fly-half Shane Drahm after only five minutes, but it did not take the home side long to respond as Ollie Smith cut a superb line off the fly-half Andy Goode to scorch in under the posts.
Goode converted to make it 7-3 to the home side before kicking two more penalties to one from Drahm to extend the lead to seven points.
Yet, as the Warriors have shown all season, they are nothing if not dogged, and another Drahm penalty, followed by a neatly taken try by Dale Rasmussen - also converted by Drahm - put the Warriors into a surprise 16-13 lead.
Goode's fourth successful kick of the night levelled proceedings just before halftime and whatever their coach, Pat Howard, had said at half-time seemed to work, as the Tigers came flying out of the blocks in the second half.
One barnstorming run by Alesana Tuilagi straight after the break led to the Warriors wing Mark Tucker being sent to the sin-bin for killing the ball. The home side immediately took advantage, working the ball to the winger from a scrum for Tuilagi to crash over in the corner.
Worcester continued to hang on and Drahm's fourth kick of the night kept them within two points with half an hour left, before another monstrous effort from the fly-half put the visitors 22-21 in front.
Roared on by their faithful supporters, Leicester forced their way back in front in dramatic fashion when Cornwell was bundled over the line with the help of his forwards.
Goode's conversion made it 28-22, but the Warriors continued to fight and were desperately unlucky not to claim a further try in the dying moments. Yet Leicester held on to record their first Premiership win in three outings.
Leicester: Tries A Smith, Tuilagi, Cornwell; Conversions Goode 2; Penalties Goode 3. Worcester: Try Rasmussen; Conversion Drahm; Penalties Drahm 5.
Leicester: Murphy; A Tuilagi, Cornwell, Smith, Varndell; Goode, Ellis; Holford, Chuter, White, Hamilton, Cullen, Moody,
Jennings, Corry. Replacements: Taikaufa, Morris, B Deacon, Johnson, Bemand, Humphreys, Dodge.
Worcester: Le Roux; Trueman, Rasmussen, Lombard, Tucker; Drahm, Gomarsall; Windo, Hickie, Tuamoepeau, Murphy, Gillies, Horstmann, Harding, Hickey. Replacements: Van Niekerk, L Fortey, O'Donoghue, Vaili, Powell, Hylton, Whatling.
Referee: D Rose (RFU).Reuse content