But it wasn't all good news for the Blues, as Cesc Fabregas missed a penalty in what appears to be his final game for the club.
Maurizio Sarri named Ruben Loftus-Cheek in his starting line-up and made Fabregas captain for the day, but it was Morata and Callum Hudson-Odoi who impressed for the Blues as the pair combined for both goals at Stamford Bridge.
Fabregas had the chance to bow out with a goal before his rumoured move to Monaco, but had his first-half spot-kick saved. Morata struck twice inside 10 second-half minutes, aided by the impressive Hudson-Odoi, whose own future has been at the centre of intense speculation this week amid confirmed interest from Bayern Munich.
Loftus-Cheek was replaced after just 42 minutes as he struggled with a back injury on an afternoon of mixed fortunes for Chelsea's players on an individual level, while Sarri's men comfortably dispatched Aitor Karanka's well-organised Forest side.
Morata's struggle to find the net this season was summed up after 12 minutes when Davide Zappacosta's cross afforded him a free header from six yards out and the Spaniard headed straight at Luke Steele despite having the whole goal to aim at.
Morata appeared to be brought down by Claudio Yacob when the Forest defender was the last man only for the referee to wave Chelsea's appeals for a free-kick away, and, moments later, Yacob made a vital block to prevent Hudson-Odoi from opening the scoring.
When Loftus-Cheek was hacked down by Danny Fox on the half-hour mark, the moment looked made for Fabregas, but his staggered run-up to the penalty failed to fool Steele, who dived down to his right to push the ball around the post.
Hudson-Odoi showed why he is one of the Premier League's hottest talents when he burst down the right side of the penalty area four minutes into the second half and whipped in a cross that Morata met with an instinctive side-footed finish at the near post to give Chelsea the lead.
The teenage winger almost got one himself when he danced into the box only to see his shot blocked by a good low save by Steele. But he was unstoppable on the wing just before the hour when he sent a cross sailing to the far post where Morata looped a header beyond Steele to double Chelsea's lead and put the game beyond Forest, which was toothless in attack and showed no sign of mounting a comeback.
The afternoon's last notable moment saw Fabregas given a standing ovation as he left the field in the 85th minute, the Chelsea faithful rising to acknowledge a man who has helped the club to two Premier League titles in a trophy-laden four-and-a-half years at the club.
Fabregas returned to the pitch after the full-time whistle and was visibly emotional as he paid tribute to the Chelsea fans.