The opening few rounds provided a tentative affair, as both men attempted to weigh each other up without making too many inroads.
Murray did improve as things went on, though, forcing Groves into the corner on a few occasions in rounds four and five, with one jab cutting the Hammersmith boxer's right eye.
Groves was however proving tricky to catch, allowing him to move in on Murray who was forced onto the ropes in round six at the O2 Arena.
A wild Murray punch followed in the seventh, paving the way for Groves to launch an onslaught of his own, and it was clear that the St Helens native was struggling for energy.
That left Groves in the driving seat if things were to go the distance, and indeed they did as a flurry of punches from Murray proved too little to sweep his opponent off his feet.
With the fight going all the way the judges unanimously scored the fight the same - 118-110 in favour of Groves who was left celebrating inside the ring.