Wanderers went into the contest having lost six out of seven Premier League games at the Reebok Stadium this term, and they fell behind in the 33rd minute when Albrighton prodded in Gabriel Agbonlahor's cross.
Petrov then added to the Trotters' woes six minutes before the break with a strike that went in off former Villa man Gary Cahill, and although Ivan Klasnic reduced the deficit 10 minutes into the second half, the hosts could not salvage a point.
As well as being their seventh home defeat, this was Bolton's 12th loss overall from 15 league fixtures.
They were booed by their disgruntled fans, something recently heard from Villa supporters, who will be feeling more positive after seeing their team - now up to eighth - record their first away win of the season and only their second victory in eight matches.
Bolton boss Owen Coyle made two changes to his first XI, Darren Pratley and Tuncay Sanli coming in for the benched Fabrice Muamba and injured ex-Villa man Nigel Reo-Coker, with Cahill keeping his place to face his old side after his red card in Wanderers' 3-0 defeat to Tottenham last weekend was rescinded.
Villa's team showed three adjustments from the 1-0 loss to Manchester United, manager Alex McLeish recalling Charles N'Zogbia - a week after dropping him for a breach of club rules - at the expense of Barry Bannan, and replacing injured duo Shay Given and Jermaine Jenas with Brad Guzan and Petrov.
After respects had been paid around the ground to former Bolton midfielder Gary Speed with a minute's applause, it was the hosts who created the first real chance of the game when Chris Eagles swung a free-kick towards the box and Cahill headed into Guzan's arms.
Eagles side-footed weakly at Guzan from Klasnic's lay-off before Villa squandered a good opportunity, Cahill's slip allowing N'Zogbia to cross to Petrov, who was right in front of goal but put his shot wide.
Moments later, it was Darren Bent failing to convert when he really should have scored, the unmarked striker seeing his effort come back off the legs of Jussi Jaaskelainen.
Bolton were bizarrely awarded a free-kick in a useful position after Kevin Davies appeared to shove over Alan Hutton and it was taken by Eagles, whose strike was spilled by Guzan before the danger passed. N'Zogbia then attempted to guide the ball in following a short corner, but his effort was off target.
Wanderers were struggling to contain their opponents' attacking play and it came as little surprise when Villa made the breakthrough just after the half-hour mark, Albrighton on hand to tap in Agbonlahor's delivery from the left.
Within six minutes, the visitors had doubled their lead, Petrov's drive taking a deflection off Cahill on its way in.
Bolton might have pulled one back two minutes before the break, but Guzan did well to block Kevin Davies' header.
The hosts showed more purpose at the start of the second half and after Guzan had dived to push away a curler from Eagles, Wanderers made it 2-1.
Klasnic pounced in the 55th minute, sweeping in his seventh goal of the season after Zat Knight's shot had caused a scramble in the box.
Bent was then guilty of further profligacy with a glaring miss, allowing the Trotters go on the hunt for an equaliser, Eagles dragging a shot wide, Kevin Davies heading tamely at Guzan and Mark Davies firing over the bar.
Coyle refreshed his attack, introducing Gael Kakuta in place of Tuncay and then being forced to replace the injured Klasnic with David Ngog.
Despite their continued efforts, though, Bolton they were unable to find a leveller, with Kakuta lashing wide in the closing stages before Jaaskelainen prevented Albrighton from inflicting an even heavier defeat.