Chelsea improved after halftime. It will be interesting to see, given his immediate impact, if Conte picks Morata from the start in their next game - a trip to Wembley stadium to face title rivals Tottenham Hotspur.
Any hope of an unlikely comeback looked to have disappeared when midfielder Cesc Fabregas was red-carded in the 81st after receiving his second booking.
With the clock winding down, David Luiz connected with a flick from Morata and pounded the ball into the goal for Chelsea's second of the game.
There were concerns surrounding the champions leading up to the big kick-off, with manager Antonio Conte voicing his concerns over a thread-bare squad. Chelsea are also without Eden Hazard, Pedro and Tiemoue Bakayoko, who are all injured, and they sold Nemaja Matic this summer to Manchester United.
"After the red card we lost our composure and we conceded three goals".
Reigning champions Chelsea is all set to defend their Premier League crown when they welcome Burnley at Stamford Bridge on Saturday afternoon.
However, the title holders' chances of getting something out of the game were dealt yet another blow when Cesc Fabregas was sent off for a second yellow after a challenge on Jack Cork.
Conte is desperate for reinforcements in the final three weeks of the transfer window. "He needs to develop, but for sure he is trying to put his best in every moment of the day".
"I'm not anxious because we have to trust in our work".
"It can happen, but we must pay attention and try and think there is the rest of the game to do our best".
Chelsea were without a number of key players, and the team selected by Conte highlighted the lack of depth now in the squad. And your first away win is important after last season [not getting one until April], so it kills a few things off early doors.