Morata toiled for scant reward as Chelsea were rebuffed during a frustrating opening 45 minutes but he gleefully headed home a pinpoint Cesar Azpilicueta delivery – the sixth time his countryman has supplied an assist to him this season – within a minute of the restart.
Marcos Alonso further added to the Spanish flavour with Chelsea's second, while Cesc Fabregas was easy on the eye in midfield as the reigning champions closed to within a point of Manchester Untied in second.
"Morata is our number nine and is important," Conte said, as quoted by BBC Sport.
"Today he played a good game with and without the ball, his commitment was great. But I'm happy with the commitment of all my players."
Morata was absent through suspension as Chelsea had 25 shots without success in a 0-0 draw at Everton last time out and Conte feared his team were on course for similar frustration as Brighton held firm at halfway.
"In the first half we had the right chances to score but didn't take them," he said, having lost defender Andreas Christensen to illness before the match. "For this reason it becomes difficult because your opponent stays with 10 players behind the ball.
"In the second half we settled very well and created many chances. It was a good performance with good intensity.
"It's the same performance against Everton – against Everton we showed 25 times we had shots on goal but today we scored twice. We are in a good moment of form and just continue this way."
This time last year, Chelsea had the title race in the palm of their hand, but Conte is happy to concede runaway leaders Manchester City have altered the terms of battle this time around.
"This season is different to last season," he added, with City in a position to go 15 points clear at the summit if they beat Newcastle United on Wednesday.
"Last season a lot of times we won games and were a bit lucky – like against West Brom here, Sunderland. This season sometimes we could have more luck.
"We have great respect for Manchester City because they are doing an extraordinary thing."
Brighton pushed gamely to get back into the match through Glenn Murray and Shane Duffy late on, but forthcoming matches against Newcastle, Bournemouth and West Brom are likely to have a greater bearing on their fate.
"We need to figure a way of getting the goals we need," said their manager, Chris Hughton.
"We're very conscious of the division we're in. What we will do is work as hard as we can coming up in January to strengthen the squad in areas that can strengthen us."