James's brace came inside the first 11 minutes, with Zinedine Zidane's men barely breaking sweat against wholly overmatched opponents.
Morata's double was also the fruit of a quickfire effort after the half-hour, from which point Madrid were able to take their foot off the gas with far more testing assignments ahead.
Atletico are up next, with the European champions' 3-0 advantage from the first leg of the all-Madrid UEFA Champions League semi-final likely to be ample insurance.
Madrid remain behind Barcelona in LaLiga by virtue of an inferior head-to-head record, but have a game in hand, meaning matches at home to Sevilla and away at Celta Vigo – both teams who have beaten Zidane's men this season – are likely to be pivotal to the outcome of the title race.
Barcelona were 4-1 winners against Villarreal earlier in the day and their rivals went ahead within three minutes at Nuevo Los Carmenes, picking the hosts apart with inevitable ease.
Morata threaded a pass through an inviting gap on the left-hand side of the Granada backline and Lucas Vazquez charged into the box.
Lucas fired across goal and James wheeled away in celebration, although the decisive touch arguably came off Granada centre-back Sverrir Ingason.
There were no doubts over James's claims to Madrid's second eight minutes later.
Vazquez overhit a cross but Fabio Coentrao was allowed to retrieve the ball on the left and send it back towards the area, where the Colombia playmaker was given similarly ample room to head home.
The dire start persuaded Granada boss Tony Adams to make a tactical switch in the 18th minute, with defensive midfielder Uche replacing winger and fellow Watford loanee Aly Malle.
That stemmed the tide to an extend but Morata got himself on the scoresheet with half-an-hour played, crashing in via the underside of the crossbar after fullback Danilo streamed clear down the right flank.
It was two in five minutes for the Spain striker – Marco Asensio sauntering towards the Granada area to find his team-mate in the box, where Morata twisted Martin Hongla to distraction before blasting past Guillermo Ochoa.
Lucas cut in from the right to fire against the top of the crossbar in the 42nd minute and forced a one-on-one stop from Ochoa, with Casemiro lifting the rebound over.
Despite that relative damage limitation, Granada departed to predictable boos at the interval.
Adams sent out his players with relatively renewed purpose after the break, Lucas firing into the side-netting as his quest for a goal continued.
Karim Benzema was introduced in place of Asensio before the hour and he almost scored on the end of Vazquez's return pass in the 61st minute, with Danilo drilling the rebound against the base of the post.
Madrid captain Sergio Ramos was denied by Guillermo from a James corner and prodded wide at the near post in the 66th minute after Lucas again shot goalwards in vain.
Martin Hongla blazed over 10 minutes from time and on-loan Borussia Dortmund forward Adrian Ramos forced Kiko Casilla into a rare save at his near post as Granada sought consolation on a night in keeping with a shambolic season on and off the field.