Reading took the lead with only four minutes gone when Pavel Pogrebnyak got a touch to Garath McCleary's nod-down to divert the ball past Cardiff goalkeeper David Marshall.
But they allowed a mediocre Cardiff side to snatch a point in the 90th minute when McAleny rifled in a shot from Aron Gunnarsson's precise pass.
Reading face an FA Cup semi-final against Arsenal on April 18 but they had won only two of their previous nine Championship matches coming into this one, losing six of them.
Cardiff's season has been one of inconsistency, too, but they arrived at the Madejski Stadium on an unbeaten run of three matches. They were also undefeated on their travels for five games, winning their past three.
Reading made the early running and were rewarded in only the fourth minute when they went ahead. Jordan Obita crossed from the left, McCleary nodded it forward and Pogrebnyak guided it past Marshall for his third goal in two matches.
Cardiff, beaten 2-1 at home by Reading in the cup fourth round in January, replied quickly. McAleny tried a snapshot from the edge of the Reading area but his effort was half-blocked and goalkeeper Adam Federici gathered comfortably.
Reading could have stretched their lead when captain Alex Pearce rose to meet a McCleary corner but fellow centre-back Michael Hector got there before him and glanced his header wide.
Cardiff tried hard to get back into the game but had little joy. Fabio cut in from the left flank but his powerful strike was blocked by Pearce at the near post, and Peter Whittingham's dangerous free-kick was neatly caught by Federici.
Reading continued to assert control after the break, with Chelsea loanee Nathan Ake impressing on his debut in midfield. Most of Reading's best creative moves were channelled through him.
Cardiff relied on the swift counter-attack, with Joe Ralls almost setting free McAleny. But his final pass carried too much pace and, with McAleny unable to retrieve it, the chance went begging.
An opportunity also went astray at the other end, when Bruno Ecuele-Manga's poor pass was intercepted by McCleary but the Reading winger hesitated too long before firing a shot wide of Marshall's far post.
Cardiff responded with a low shot from Craig Noone, which Federici did well to save, and a header from Ecuele-Manga from another Whittingham free-kick, which drifted wide.
Reading went much closer in the closing stages. Substitute Kwesi Appiah, on debut on loan from Crystal Palace, forced a fine stop from Marshall and Hector nodded a McCleary corner into the ground and up against the crossbar.
But Cardiff grabbed a draw right at the end from McAleny's fine finish from the edge of the home area.
Reading: Federici, Gunter, Pearce, Hector, Obita, McCleary (Norwood 74'), Ake, Akpan, Robson-Kanu (Blackman 85'), Mackie (Appiah 68'), Pogrebnyak
Subs not used: Yakubu, Karacan, Knight, Andersen
Goals: Pogrebnyak 4'
Cardiff: Marshall, Peltier (Malone 84'), Ecuele Manga, Morrison, Da Silva, Noone, Whittingham, Gunnarsson, Ralls (Kennedy 65'), Doyle (Mason 65'), McAleny
Subs not used: Adeyemi, O'Keefe, Moore, Gabbidon.
Goals: McAleny 90'
Referee: Scott Duncan