Brighton set up a Carabao Cup fourth-round clash with Manchester United as they eased past Preston 2-0 at Deepdale.
Jahanbakhsh left Preston goalkeeper Connor Ripley with little chance when he rifled home a powerful shot just before the hour – and Mac Allister made sure when he thumped home from Pascal Gross' pull-back a little over quarter of an hour later.
Preston were left to rue a Patrick Bauer header which struck the crossbar in the first half but could have few complaints as Brighton finished the game the stronger of the two sides.
Graham Potter turned once more to what might be called his League Cup side, making 11 changes from the 3-0 win at Newcastle on Sunday but including nine of those who started last week's win over Portsmouth and handing starts to Haydon Roberts and Max Sanders.
Alex Neil, having fielded a strong side in the 2-1 win over Derby in the previous round, also made several changes with Bauer and Joe Rafferty the only two in the starting XI who also faced Norwich on Saturday.
Preston started the stronger of the two sides but could not test Jason Steele. The 18-year-old Roberts, subject of recent interest from Leeds, looked assured alongside Dan Burn in the centre of the Brighton defence as the visitors slowly grew into the game.
More than half an hour had gone until either side had a clear sight of goal, with Jahanbakhsh beating the offside trap to bring a strong save from Ripley at his near post.
Preston were next to threaten eight minutes before the break. Brad Potts powered forward, playing the ball in to Jayden Stockley who took a touch to step inside Burn before hitting a low shot that Steele did well to turn around the post.
From the resulting corner Bauer headed against the bar.
Brighton threatened again just before half-time as the ball broke for Mac Allister but Ripley was able to turn his shot behind.
It set the tone for the second half as Brighton increasingly took control. Mac Allister turned a shot narrowly wide from the edge of the area before Viktor Gyokeres sent a long-range drive wide.
The breakthrough came just before the hour. Bernardo's searching cross made it all the way across the area to find Jahanbakhsh at the far post and the Iranian sent a powerful shot past Ripley.
Mac Allister – who like Jahanbakhsh was among the scorers in last week's 4-0 win over Pompey – then made sure in the 75th minute, given the easiest of tasks to finish after Gross made space on the byline to pull the ball back.