Despite the win, the two-time African champions sit at the bottom of Group D, just one point shy of second-place Al Masry from Egypt with two matches left to play.
The top two teams from each group will move on to the knockout stage, and Enyimba is aiming to be the first Nigerian club to take home the trophy.
Next Sunday, Enyimba will face Masry in Uyo, looking to bounce back from a 2-0 defeat in North Africa last November.
After a series of disappointing results, including a 3-0 loss to the Bulls last month, the club decided to switch coaches, bringing in veteran Stanley Eguma to replace Yemi Olarenwaju.
Atule scored the opening and final goals of the match, with Ifeanyi Ihemekwele and Brown Ideye also finding the net for Enyimba, who had only managed two goals in their previous five qualifying and group matches.
The Bulls' lone goal came from Nigerian Ejaita Ifoni, who equalized before Ihemekwele put Enyimba ahead 2-1 at halftime in this African version of the UEFA Europa League.
Egypt's title-holders Zamalek lead the group with eight points after a 0-0 draw against Masry, while Masry has five points, and both Bulls and Enyimba have four.
In another match, South African team Stellenbosch, one of six debutants in the group, kept their quarter-finals hopes alive with a 2-0 win over Angola's Desportivo Lunda Sul in Pretoria.
Former New Zealand midfielder Andre de Jong scored both goals, breaking the deadlock in the 50th minute and converting a penalty later on.
Renaissance Berkane from Morocco also secured a spot in the quarter-finals with a 1-0 victory over Stade Malien from Mali. Stellenbosch can also qualify if they beat Stade next Sunday.
Meanwhile, Tanzanian team Simba edged out three-time Confederation Cup champions CS Sfaxien from Tunisia with a 1-0 win in Rades, putting them level at the top of Group A with Algeria's CS Constantine, both on nine points.
This represents the fourth consecutive group stage defeat for Sfaxien, following the recent dismissal of Portuguese manager Alexandre Santos.