Botica struck two minutes from time to give Quins a 22-20 away victory over the Scarlets and clinch a consolation prize of an Amlin Challenge Cup quarter-final place.
Quins, already out of Heineken Cup last-eight contention, moved into the Amlin knockout phase along with Northampton and Gloucester by prevailing in west Wales and securing one of three Amlin spots for Heineken group runners-up.
“It was harem-scarem out there,” Quins rugby director O’Shea said. “It is a delight to play against a team like the Scarlets, it really is. Both teams tried to play in a way that should be lauded.
“I thought we controlled the last six minutes of the game brilliantly. I am baffled that we didn’t get more penalties at different times, but I thought the referee, overall, did a really good job.”
Wales centre Scott Williams looked to have claimed the Pool Four encounter’s decisive touchdown, which followed earlier Scarlets tries by scrum-half Gareth Davies and flanker Aaron Shingler, while Rhys Priestland kicked a penalty and conversion.
Quins scored three tries of their own – full-back Mike Brown, wing Ollie Lindsay-Hague and scrum-half Karl Dickson the scorers – and Nick Evans booted two conversions during a game which the visitors led 14-7 and 19-15 before they finally sealed victory.
Scarlets scorers: Tries: G. Davies, A. Shingler, S. Williams. Cons: Priestland. Pens: Priestland.
A. Thomas, K. Phillips, Maule, S. Williams, J. Williams, Priestland, G. Davies, John, E. Phillips, Lee, Ball, Earle, A. Shingler, Barclay, McCusker.
Replacements: Turnbull for John (58), Adriaanse for Lee (77), Snyman for Earle (55), Evans for Barclay (58).
Harlequins scorers: Tries: Brown, Lindsay-Hague, Dickson. Cons: Evans 2. Pens: Botica.
Brown, Lindsay-Hague, Hopper, Molenaar, Monye, Evans, Dickson, Marler, Ward, Collier, Kennedy, Robson, Guest, Robshaw, Easter.
Replacements: Williams for Lindsay-Hague (58), Botica for Monye (65), Stuart for Evans (77), Matthews for Kennedy (55), Fa’asavalu for Guest.
Jerome Garces (France).