The presence of Manchester United manager Sir Alex Ferguson in the stands at London Road appeared to inspire son Darren's hosts, who dominated the first half before soaking up prolonged spells of pressure in the second to secure three crucial points.
Tomlin gave Ferguson's side the early advantage after seven minutes, heading into an empty net after George Boyd's initial effort was hacked off the line.
Peterborough were unlucky not to go into the break with a more comfortable lead after Gabriel Zakuani nodded against the crossbar from Grant McCann's corner.
Ball scored the hosts' second after 62 minutes with a superb solo goal and Tomlin tapped home late on to wrap up the win.
Ferguson returned Tomlin to his starting line-up, while Paul Jones replaced Joe Lewis in goal.
City were buoyed by the return of Kalifa Cisse from a knee injury, while Brett Pitman was restored up front by boss Derek McInnes.
Despite their poor recent form, Posh enjoyed a flying start and took the lead after just seven minutes.
Ball sent in a cross, Boyd's excellent first touch allowed him to get a shot away and, although that effort was cleared off the line by Liam Fontaine, Tomlin was on hand to nod the ball into an unguarded net.
City struggled to create any chances in the first half-hour, and David James in the Robins goal had to be alert to save Ball's low effort before the claiming the ball at the striker's feet.
And with 13 minutes remaining of the opening period, Posh were within inches of adding a second.
McCann's corner from the left picked out Zakuani, but the centre-back's thunderous header cannoned off the bar with James beaten.
Tomlin's dipping 25-yard volley just cleared the bar after 38 minutes, and all City could show for their first-half efforts was two off-target attempts from Pitman and Marvin Elliott.
McInnes changed formation at half-time, introducing Chris Wood in place of Cisse and switching to 4-4-2, and he was almost rewarded within two minutes of the second period.
First Pitman fired over from Wood's flick-on before Jones brilliantly saved Fontaine's header as the Robins pushed hard for an equaliser.
After being untested in the first half, Jones was on inspired form to deny Albert Adomah's low drive and punch clear Wood's header as the away side heaped pressure on the Posh goal.
Lee Frecklington then cleared Stephen McManus' attempt from Pitman's corner off the line, before Peterborough scored against the run of play.
Ball darted into the penalty area, tricked his way around two markers and found the top left-hand corner from 12 yards.
The second strike killed the match, and chances were at a premium in the final minutes.
Emile Sinclair somehow contrived to miss an open goal from Boyd's cut-back, but the substitute made up for his error by teeing up Tomlin with a simple chance to tap home with five minutes remaining.