Rhys Priestland added to that score along with Iestyn Thomas before King got his second. But the win could have been greater had they made the most of their kicks.
Glasgow had to make a change before kick-off when they lost captain Alastair Kellock to a knee injury in the warm-up, Dan Turner came in to replace him.
The opening exchanges were scrappy but it was the visitors who were showing more potential. And they had an early chance to take the lead with a penalty after five minutes, only for Colin Gregor to kick short.
Scarlets’ Priestland showed him how to do it on 12 minutes when Andy Newman was penalised for a high tackle. However, he did need help of the crossbar to get the ball over and that was the shape of things to come as his kicking let him down throughout the game.
Glasgow were then reduced to 14 men when John Beattie was sin-binned for failing to roll away, but Priestland missed his second of two kicks inside a minute. And that looked to prove costly as Pinder spotted a gap in the Scarlets defence to go over after patient build-up by the visitors to give them a 5-3 lead.
Gregor converted, but that lead was cut within four minutes when scrum half Cattle went over down the other end from a drive. Priestland made no mistake this time.
Four minutes before the break, Scarlets made it 15-7 after a move started by Morgan Stoddart. He made a great run from halfway to five metres from Glasgow’s try-line before the ball was freed across to King to go over in the corner for his sixth Magners League try of the season.
Priestland missed the conversion along with another penalty before the half was out but was helped by Glasgow lacking any real threat.
Ten minutes into the second-half, two errors by Glasgow saw the Scarlets break and Priestland squeezed over in the corner, but failed to convert. Replacement Ed Kalman then became the second Glasgow player to receive a yellow card after they had been warned against persistently giving away penalties by referee George Clancy.
Prop Iestyn Thomas extended the Scarlets’ lead to 25-7 on the hour with a bonus point try after more poor defending from Glasgow. Stoddart took over kicking duties from Priestland, only for him to miss too.
King grabbed his second try of the game with five minutes remaining to seal a convincing win. Ceiron Thomas missed the conversion but by now, it did not matter.
