In freezing conditions, the 20-year-old scored 1-8 as the two-time winners, managed by Clare supremo Davy Fitzgerald, set up a Limerick derby at UL next week.
Kelly fired home a second-half penalty, converted six frees and added two superb points from play to seal LIT’s safe passage to the last eight of the competition.
But LIT had to work hard for the win on home soil against a GMIT side reduced to 14 men midway through the first half.
Corner-forward Gerry Hennelly was dismissed for striking LIT corner-back Cian Nolan off the ball.
GMIT were 0-0 to 0-2 in arrears when Hennelly saw red but at half-time, they were just a point behind, 1-1 to 0-5.
Playing with the breeze, GMIT scored the only goal of the first half as Padraig Flanagan’s speculative shot from the left flank was adjudged to have crossed the line.
But, with the breeze at their backs in the second half, LIT upped the ante as Kelly called the tune.
The Ballyea dynamo cracked home a 53rd-minute penalty to make the game safe before Galway underage star Shane Moloney, who scored 1-5, found the net from a 20m free with just three minutes left.
Scorers for LIT: T Kelly 1-8 (1-0 pen, 0-6f), S O’Brien & C McInerney 0-2 each, S McGrath & J Whelan 0-1 each.
Scorers for GMIT: S Moloney 1-5 (1-2f), P Flanagan 1-0.
LIT: A Murphy (Limerick); S O’Gorman (Clare), M Minihan (Tipperary), C Nolan (Clare); P Flaherty (Galway), B O’Connell (Limerick), E Boyce (Clare); S O’Brien (Limerick), T Kelly (Clare); P Begley (Limerick), M Gennery (Tipperary), P Ivors (Tipperary); S McGrath (Clare), C McInerney (Clare), O Hickey (Clare).
Subs: P Robinson (Galway) for Ivors (43), D Whelan (Clare) for Hickey (45), G Guilfoyle (Clare) for McGrath (45).
GMIT: J Egan (Offaly); B Hunt (Mayo), Tomas Kenny (Galway), P Fox (Galway); G Grealish (Galway), Kevin Lane (Galway), P Hoban (Galway); D McGreal (Galway), P Flanagan (Galway); N Keary (Galway), J Kilkenny (Kiltormer), C O’Donnell (Clare); G Brennan (Galway), S Moloney (Galway), G Hennelly (Galway).
Subs: S Lawless (Galway) for Brennan (40), Brennan for McGreal (55).
Referee: J O’Brien (Tipperary).