Peterborough's club record signing showed exactly why manager Darren Ferguson splashed out £1.2 million to sign him from Watford in the summer, at a time when O'Driscoll wanted him on loan.
Assombalonga's strike to make it 2-0 early in the second half will live long in the memory. Receiving the ball outside the right hand corner of the box he drilled an unstoppable left-footed shot into the opposite top corner of the net.
Tyrone Barnett had fired Posh in front after 24 minutes when City goalkeeper Frank Fielding failed to hold Craig Alcock's 20-yard drive. And Assombalonga capped a man-of-the-match display with a strong solo run and deft finish two minutes from time.
O'Driscoll said: "If he hits a better shot in his entire career I'll eat my hat.
"We were interested in signing him, but could only do so on loan, while Peterborough came up with the money. So we were aware of his talent.
"A goalkeeping error has put us behind after we made a decent start to the game and that one early in the second half set us back again.
"The third goal was a poor one from our point of view, but by then the damage was done. Our forward players did not do as well in the game as theirs."
Peterborough would have won by an even wider margin had Fielding saved a 27th-minute penalty from Lee Tomlin after a reckless challenge by James O'Connor on Assombalonga.
In the closing minutes Assombalonga set up a great chance for Barnett only for his strike partner to shoot over.
City only threatened at the death and were left still seeking a first league win of the campaign following relegation last season.