Carolina (1-0) controlled play at the onset of the game and that ultimately paid dividends when Engel finished from 15 yards in the 19th minute off a feed from Craven.
Minutes later Cal was on the cusp of an equalizer but senior All-America defender Boyd Okwuonu cleared away a ball on the goal line that was going to tie the match in the 21st minute.
Tar Heel defender Jonathan Campbell nearly made it 2-0 with a header off a corner kick, but the Bears defense stood tall to keep the ball from crossing the line.
Just three minutes later, Craven beats the Cal keeper for that two-goal advantage in the 33rd minute. Lovejoy earned the assist as he placed a nice through ball to the foot of Craven.
Cal (0-1) cut its defect in half with a goal from reserve Christian Thierjung in the 36th minute. That was the final tally of the opening half with Carolina taking a 2-1 lead into intermission.
UNC All-ACC keeper Brendan Moore made three brilliant saves in the first 18 minutes of the second half to keep his club on top. He pushed aside a header in the 46th minute, stopped a point-blank shot from Connor Hallisey in the 53th minute and later did the same to Stefano Bonomo in the 63rd minute.
The Tar Heels regained its composure over the final 20 minutes. Lovejoy iced the match with a blue-collar goal in the 83th minute to cap the scoring, 3-1, in favor of Carolina.
Moore was forced to come up with eight saves on the evening, while Cal's Kevin Peach had four saves over 90 minutes.
Carolina held a 17-13 shot advantage over the Golden Bears, while Cal had seven corners to the Tar Heels five.
UNC hosts No. 1 UCLA on Sunday at 7 p.m. The Bruins earned a 3-1 victory over Wake Forest this evening.