"Things came together in 10 good minutes for us in the second half. I'd like to think that it's not a typical Leinster performance, but at least we came back.
"We need to start stronger, especially away from home. It was important to keep the pressure on other clubs at the top of the table and the crowd were absolutely fantastic tonight."
But with Owen Finegan and Christian Warner, whose introduction forced Contepomi to inside centre, coming off the bench, Leinster turned the game.
A Contepomi penalty was followed up by a 58th-minute try from pacy winger Brown, which brought the sides level. Then Lewis shrugged off a Barry Davies tackle to romp over on a 40-metre run.
Keogh ended a great spell of pressure to dive over from close range and Heaslip followed suit, on 68 minutes.
Contepomi managed to convert all four tries for an incredible score line of 44-20, and there was still time for two late Scarlet tries.
LEINSTER SCORERS: J. Heaslip (2 tries), G. Brown / K. Lewis / S. Keogh (1 try each), F. Contepomi (3 penalties, 5 conversions)
LLANELLI SCORERS: B. Davies (1 try, 2 conversions), M. Stoddart / R. King / C. Stuart-Smith / D. James (1 try each), C. Thomas (1 penalty, 1 conversion)
15: Ross McCarron (Niall Ronan, 73)
14: Gary Brown
13: Kieran Lewis
12: Mick Berne
11: Luke Fitzgerald (Christian Warner, 55)
10: Felipe Contepomi CAPTAIN
9: Guy Easterby (Chris Whitaker, 65)
1: Stanley Wright (Reggie Corrigan, 70)
2: Bernard Jackman (Brian Blaney, 70)
3: Will Green
4: Trevor Hogan (Devin Toner, 77)
5: Cameron Jowitt (Owen Finegan, 44)
6: Stephen Keogh
7: Keith Gleeson
8: Jamie Heaslip
15: Morgan Stoddart
14: Dafydd James
13: Regan King
12: Matthew Watkins
11: Darren Daniel
10: Ceiron Thomas
9: Clive Stuart-Smith
1: Iestyn Thomas
2: Ken Owens
3: Craig Dunlea
4: Vernon Cooper
5: Scott MacLeod
6: Dafydd Jones
7: James Bater CAPTAIN
8: Nathan Thomas
16: Deacon Manu
17: Aled Gravelle
18: Adam Jones
19: Inoke Afeaki
20: Liam Davies
21: Barry Davies
22: Garan Evans
REFEREE: Malcolm Changleng (SRU), SUB REFEREE: Olan Trevor (IRFU), TOUCH JUDGE: Peter Ferguson (IRFU), 4th OFFICIAL: Peter Dennehy (ARLB), 5th OFFICIAL: Tom Tuohy (ARLB)