Ricketts marked his return from more than 10 months out injured with a stunning first-half strike in Saturday's Premier League clash.
The full-back, making his first appearance since rupturing an Achilles in February, had never scored for Bolton before but he showed a striker's eye for goal in the 22nd minute with a fine curling shot into the far corner from 25 yards.
Bolton deserved their half-time lead despite Stephen Ward's thunderbolt against the bar but Wolves levelled less than four minutes into the second period when Steven Fletcher headed home Matt Jarvis' free-kick.
Defender Gary Cahill captained the side despite a fee having been agreed with Chelsea, and he received a warm reception from fans when his name was read out.
Bolton had looked nervous and short on confidence in their 2-0 defeat by Newcastle on Boxing Day, making this really a must-win game, particularly given Blackburn's shock victory at Manchester United, which left the Trotters bottom at kick-off.
Manager Owen Coyle had called for his side to show more character following Monday's loss and this time they came up with the goods, playing with greater assertiveness and attacking at speed down the flanks.
They still did not create too many opportunities early on, and when they did David Ngog shot tamely at Wayne Hennessey and Ivan Klasnic was denied by good defending from Richard Stearman.
Bolton got the goal their play deserved midway through the half, and it was a moment of real quality from Ricketts, who picked up the ball in space 35 yards out and drove forward before curling a brilliant effort past Hennessey.
Wolves had offered little in attack but they came within a whisker of equalising 12 minutes before the break when Ward let fly from 25 yards and his shot smacked against the crossbar.
Petrov was proving a key figure down the left for Bolton and another surging run took him to the byline before he cut the ball back for Klasnic, whose shot into the ground produced a smart stop from Hennessey.
Wolves boss Mick McCarthy made a substitution at half-time, sending on Dave Edwards for George Elokobi, and within four minutes the visitors were level.
Wolves won two free-kicks in quick succession and from the second Jarvis sent in a wicked ball that Fletcher headed in from close range with Jussi Jaaskelainen rooted to the spot.
It was an eighth goal of the season for the Scot, who was brought to England in 2009 by Coyle when he was at Burnley.
The hosts would have been back in front in the 55th minute but for a super save from Hennessey, who got down brilliantly to keep out Fabrice Muamba's well-struck volley.
Bolton had not let their heads drop but Wolves were protecting Hennessey pretty well and the only shots the keeper had to deal with were a couple of poked efforts from Mark Davies.
Bolton were getting closer and, after Christophe Berra had almost diverted the ball into his own net under pressure from Ngog, Steinsson drew another clawing save from Hennessey with a header from Petrov's corner.
Both managers made changes up front, with Kevin Doyle coming on for Fletcher while Tuncay Sanli replaced Klasnic, and it was the Wolves man who almost made the breakthrough in the 81st minute but his header from Stephen Hunt's cross was well blocked by Jaaskelainen.
Bolton had not drawn a Premier League match since February and it was not the result they wanted, but it could have been worse had a combination of Mark Davies and a post not kept out Tuncay's wayward header in front of his own goal.
Tensions were growing and Jaaskelainen and Zat Knight had a set-to after the keeper declined to come out to collect a throughball, while Jaaskelainen then did well to get a hand to the ball as Doyle found himself through one-on-one.