After a goalless first half in Agadir, 24-year-old Berkaoui broke the deadlock on 50 minutes.
He struck twice more before the hour and the result confirmed Agadir as favourites to win Group D and face a quarter-final against the runners-up in one of the other three.
El Berkaoui netted twice before in the Confederation Cup this season and his five-goal tally is one less than the leading scorers, South African Gift Motupa and Burkinabe Eric Traore.
The fastest hat-trick in a CAF club match was scored by Zambian Lazarous Kambole, who took five minutes to achieve the feat for Zesco United in the 2018 CAF Champions League.
It was only the second hat-trick scored in 32 matches in the group phase of the African equivalent of the UEFA Europa League.
The other also came in Group D, and just a few hours earlier, with Stanley Dimbga scoring a treble as Enyimba of Nigeria swept aside Paradou of Algeria 4-1 in Aba.
Dimbga needed 62 minutes to complete a hat-trick that began in the 15th minute, and he netted again one minute after Victor Mbaoma scored to earn Enyimba a 3-0 half-time advantage.
The most successful Nigerian club in CAF competitions, with four titles, went further ahead before Abdelhak Kadri claimed a late consolation goal for the Algerians.
– Pyramids first qualifiers –
Agadir have 10 points, Enyimba six, Paradou four and San Pedro two with two matchdays remaining, and the top two finishers advance to the knockout stage.
Meanwhile, expensively assembled Pyramids became the first qualifiers for the quarter-finals thanks to a 2-0 win over fellow Egyptian side Al Masry in Cairo.
Traore broke the deadlock midway through the opening half and Nabil Emad ensured Pyramids kept a perfect Group A record with a second goal on 71 minutes.
A poor campaign by former CAF title winners Enugu Rangers of Nigeria reached a new low when they needed a penalty to draw 1-1 at home against minnows Nouadhibou of Mauritania.
After holding Nouadhibou in Nouakchott two weeks ago, Rangers were expected to win in Enugu and apply pressure to Masry in the chase for the second qualifying slot.
But Nouadhibou, the first Mauritanian club to reach the group stage of a CAF competition, took the lead during the first half through leading scorer Yassin el Welly.
Ibrahim Olawoyin levelled from a 68th-minute spot-kick, but the home team failed to score again and trail Masry by four points.
Confederation Cup debutants Pyramids have 12 points, Masry six and Enugu and Nouadhibou two each.
In Group B, Renaissance Berkane of Morocco clung to first place despite a 1-0 defeat by Daring Club Motema Pembe of the Democratic Republic of Congo in Kinshasa.
Horoya of Guinea stayed top of Group C by forcing a 0-0 draw at second-place Djoliba of Mali in Bamako while Al Nasr of Libya overcame Bidvest Wits of South Africa 2-1 in Cairo.
