The Royals saw their Premier League dream shattered by Swansea in a 4-2 defeat at Wembley in May but staked their claim to be among the frontrunners again this season with a fine comeback.
Former Reading striker Darius Henderson put the away side ahead before John Marquis doubled their advantage, but Manset, introduced in the 68th minute, grabbed a late double to ensure the spoils were shared.
The hosts started brightly, with Jimmy Kebe flashing a shot narrowly wide of David Forde's near post.
At the other end Hamer Bouazza jinked his way to the edge of the box before firing wide as the visitors signalled their intent.
James Henry whipped in a corner soon after and found the head of Tamika Mkandawire but his effort failed to trouble Adam Federici.
Reading's in-demand striker Shane Long, who scored 28 goals in the last campaign, had to leave the field for treatment in the 20th minute but he was reintroduced soon after.
Kebe continued to threaten with his pace, drifting past two opponents before being thwarted by Mkandawire as he lined up a shot.
Both sides struggled to maintain the pace they had set in the early stages as the first half drew to a close.
Darren Ward briefly set pulses racing again when he shoved Noel Hunt following a challenge between the two, but referee Dave Phillips kept his cards in his pocket.
Federici was called into action soon after the restart when Henry tried his luck from distance and, having parried the initial effort, the goalkeeper was quickly back on his feet to deny Marquis, though the flag had already gone up for offside.
But there was nothing he could do to keep out Henderson's header four minutes into the second half, with the lively Henry providing the cross from the left.
Henderson started his career at Reading and also returned to haunt them last season when he scored twice for Sheffield United in a 3-2 win.
Brian McDermott's side responded positively and Long did superbly well to control Jem Karacan's pass before rifling a shot against the crossbar.
Hunt came within inches of levelling the scores on the hour but could not quite make contact with Kebe's drilled cross.
But it was the visitors who struck next when, in 62nd minute, Henry and Liam Trotter linked well before laying on a cross for Marquis to provide the finish.
The experienced Ian Harte tried to rally his team-mates and fizzed in a low cross which somehow eluded everyone in the packed penalty area.
McDermott made a late double change, introducing Manset and Hal Robson-Kanu for Hunt and Karacan.
Manset gave Reading a glimmer of hope with a stunning long-range drive in the 86th minute then headed home Kebe's cross with a minute of normal time remaining.