Angol, who joined the club from Leyton Orient in the Summer, fired the Bantams in front in the 32nd minute.
The Latics thought that they had snatched a first point of the season in the dying minutes, as Dylan Bahamboula struck through a crowd of bodies from the edge of the box.
However, Carl Piergianni pulled down Angol on the byline to grant Bradford a penalty, and it was Angol to convert as he squeezed the ball beneath Daniel Rodgers.
Bradford City: O’Donnell; Cousin-Dawson, O’Connor, Canavan, Ridehalgh, Watt, Evans, Gilliead, Cooke, Angol, Cook
Oldham made changes of their own, as Jamie Hopcutt made his debut and Jamie Bowden missed out through covid-19 protocols.
Oldham Athletic: Rogers; Adams, Clarke, Piergianni, Hart, Stobbs, Cisse, Whelan, Keillor-Dunn, Bahamboula, Hopcutt
Story of the match
Following the full-time whistle, Bradford manager Derek Adams was quick to praise the supporters, describing the atmosphere as "electric", as the Utilita Energy Stadium hosted the largest attendance in the division.
But before the game could even get underway, Adams was faced with an injury crisis, with midfielders Yann Songo'o and Sutton both out injured, it was time for Evans to make a splash.
Evans' continued to be heavily involved, as some pinball in the Oldham box ended with the midfielder on the edge, but his audacious volleyed effort sailed adjacent to the target.
The Bantams first half pressure was finally awarded courtesy of Angol, as a long, searching ball met the head of Andy Cook, who nodded into the path of the unmarked Angol, and despite the tight angle, managed to half-volley the ball through the scrambling Rogers, giving Bradford a deserved lead.
This goal might've been exactly what the Latics needed however, as some nice link up play ended with Davis Keillor-Dunn, who looked to squeeze his shot beneath Richard O'Donnell, but the goalkeeper parried his effort away.
Heading into the second half, Adams' side had the opportunities to extend their lead, as a swift counter attack involving Charles Vernam and Cook ended at the feet of Angol, but he could only lash his strike woefully over.
Angol continued to be a nuisance for Bradford, as the striker fed the ball through to Cooke, and the midfielders tricky feet saw confusion between himself and Cook, before their lack of communication ended with the ball being scuffed wide.
Some sloppy Oldham defending ended with Angol once again robbing Piergianni at the back, but he could only knock his low effort wide to the relief of the Latics back line.
But it wouldn't be League Two without some late action, after all, there were six games with goals later than the 87th minute last weekend! But this game exploded into life in stoppage time, as a quick moving Oldham attack ended with Keillor-Dunn sliding the ball into the path of Bahamboula, and the agile attacker struck his shot through a crowd of bodies before sending the travelling Latics into absolute carnage, as O'Donnell could do nothing to prevent the late equaliser.
The away fans weren't celebrating for very long, as it was once again the home supporters turn to wreak havoc, as Angol spun Piergianni in the box before being dragged down, with the referee pointing to the spot.
Angol stepped up and calmly converted, despite Rogers getting a hand to his effort, with the game being immediately wrapped up with Bradford grasping the three points in a crazy match watched by over 17,000.
Adams praised his side in his post-match interview, and understandably, despite the setback of a late equaliser, Bradford never gave up.
Angol's late penalty and the resilience and grit of the defending throughout the ninety, which was only pierced in the dying moments. Adams has every right to be delighted, even if it wasn't the most vintage of performances, it shows the correct attitude to still snatch the three points.
It's not an ideal start for Oldham, with two defeats from two, but it's encouraging signs for Keith Curle, whose side played some impressive football and just struggled to breakdown the Bradford defence.
Oldham are reckoned as potential relegation candidates, but it's evident that they have the quality in the starting lineup to mount a real effort of staying up, and with the recent addition of Hopcutt, things can only surely get better for Oldham.
It's hard to argue with this. Angol was a constant nuisance for the Latics backline, using his power and pace to dominate the defence and despite missing quite a few chances, having the grit to find the two goals to grant Bradford a promising three points.