Despite Villa dominating the opening half against a team who finished 18th in last season's Championship, clear-cut chances were few and far between.
The best came 15 minutes in, when Enda Stevens played a sublime one-two with the resurgent Stephen Ireland, but the chance was wasted as the young left-back smashed his countryman's back-heeled pass well over the bar.
Another player who was trying to impress new boss Paul Lambert was Charles N'Zogbia, who put in a surprisingly industrious performance, putting in several useful balls into the box and having a low shot saved by Peterborough keeper and Villa old-boy Robert Olejnik.
The Posh's only chances of the first half came from set-pieces, but both free kicks were poor and dealt with easily by the young Villa defence, who looked comfortable from set pieces and did not look to be missing the presence of the injured Richard Dunne and the recently departed James Collins.
The scoring was opened by 19-year-old midfielder Johnson shortly before half-time, after an Eric Lichaj cross deflected into his path, leaving him with a simple finish at the back post.
Meaningful chances continued to prove elusive in the second half, despite both Lichaj and N'Zogbia coming close with early shots, and a smart tackle in the box from Zakuani stopping Andreas Weimann from getting through on goal.
The pot-shots continued from Villa, with goal scorer Johnson taking aim from 30 yards and missing the target. Lichaj, not wishing to be outdone, then tried exactly the same shot – with an identical result.
Ireland had a long-range drive saved late on, but substitute Holman stole the spotlight, scoring his second goal for the club in the 81st minute, with a brilliant strike that almost burst through the roof of the net.
Holman had another shot saved three minutes from time by substitute keeper Joe Day, who also kept out an effort from sub Graham Burke – but both teams were happy to take it easy and leave the result as it was.
A concern for Lambert will be a potential injury to promising young midfielder Chris Herd, who was replaced by Matt Lowton midway through the first half.
However, after a season of discontent at Villa Park last term fans will have been encouraged to see Lambert instilling his attacking philosophy that served him so well at Norwich.