After last week's 8-0 hammering at home to Bournemouth, Rowett shored up the Blues' backline and they held out for a goalless draw.
Read how it all unfolded in our minute-by-minute updates below.
11.46amHappy November everybody! The first game in the Championship today takes place at Molineux as Wolves, with their eye on going top of the table, welcome nearby Birmingham. Let's get straight to the team news...
11.47amWOLVES XI: Ikeme; Doherty, Batth, Ebanks-Landell, Rowe; McDonald, Evans, Henry, Clarke, Jacobs; McAlinden Subs: Flatt, Edwards, Stearman, Saville, Sako, Sagbo, Van La Parra
11.47amAnd in a graphic form, if you like that sort of thing:
A photo posted by Official Wolves (@officialwolves) on
6 minSAVE! Wolves continue to come forward and Clarke's looping header has to be tipped over the bar by Randolph. Moments earlier Rowe made an excellent burst into the area, but his cutback was intercepted by Robinson.
8 minBirmingham have done virtually nothing in the Wolves half so far. Rowett certainly won't be too pleased how little of the ball they've seen so far.
10 minTaylor penalises Clarke for an elbow on Gleeson and he can count himself quite lucky not to have been booked there.
10 minCHANCE! McAlinden has tons of space to run into and collect a hopeful ball over the top. Morrison is back with him and does enough to force him wide. McAlinden still gets a shot off, but it's a fairly comfortable save for Randolph.
11 minWolves keeper Ikeme makes a mess of a clearance and is lucky to see the ball end up at the feet of a teammate and not a blue shirt as he was well out of position.
14 minCotterill does really well out on the left to swing in a good cross under the pressure of two Wolves players. Birmingham have numbers forward as well, but Shinnie can't direct his header on target.
16 minWolves had 70% possession in the opening quarter of an hour, also getting all three of their shots on target. None were difficult saves for Randolph, though.
18 minEbanks-Landell must be hallucinating a bit because he's just sent a pass over the top to absolutely no-one. Sums up the last few minutes, which have been very quiet.
20 minWell, my prediction that there would be goals today doesn't look like it's going to come to fruition at the moment. Wolves have had a couple of half-chances, but it's been a really slow start to the match.
23 minMcDonald carelessly gives the ball away to Arthur and Rowe then brings the Wolves winger down to give the visitors a free kick in a great position...
23 minSIDE-NETTING! Arthur slams the ball into the near side-netting after Cotterill's free kick was flicked to the back post by a Wolves defender. Not sure if that was a shot or a cross, but he got it wrong whatever it was.
26 minCHANCE! Best chance of the match falls to Donaldson as he runs onto Davis's pass and fires it goalwards. The ball flies past Ikeme and you're waiting for the net to bulge, but it also goes past the post. They're the sort of chances that the lowly Blues have to take.
29 minBirmingham have enjoyed a good last 10 minutes and have another effort on goal as a free kick is cleared as far as Davis, whose first-time shot isn't well struck and easy for Ikeme.
12.48pmBy the way, if you want to follow the lunchtime kickoff in the Premier League between Newcastle and Liverpool, which has just kicked off, open this link in a new tab. Lovely jubbly.
35 minCHANCE! Doherty's clearance is inadvertently perfect for Clarke who bears down on the Blues defence. He has Henry in plenty of space to his right, but instead of passing cuts onto his left foot before his shot is blocked. Poor decision by the Wolves forward.
37 minSuperb cross into the middle by Grounds and although Donaldson is well placed, he is crowded out and can't meet it effectively.
37 minBOOKING! The first yellow card of the game is shown to Birmingham's Davis after a succession of fouls.
40 minWith five minutes until the break, Rowett will be watching from the sideline and must be delighted with the way his players have battled in the last 25 minutes or so. They were under the cosh a little at the start, but since then have arguably been the better side. They now have to make sure that they don't do anything silly before the interval.
44 minRowe's deep cross is a good one from the left and Grounds does the safest thing by heading it out for a corner.
45 minBatth is picked out at the back post and he heads the ball back into the six-yard box where a Birmingham foot swipes it away from danger.
45+1 minThere's been barely any stoppages so it'll just be one minute of added time.
1.11pmLooking at the two subs' benches, you'd have to say that Wolves have the stronger options that can come on. Top scorer Sako is sure to come on if Wolves don't break through soon and they also have Hull City loanee Yannick Sagbo available.
1.13pmWes Thomas is probably Birmingham's best attacking option, but I reckon Rowett will only bring him on and change formation if his side fall behind.
1.15pmI've probably been most impressed with young Birmingham winger Arthur so far. He's looked bright on the ball and has caused Wolves the odd problem going forward. Blues debutant Morrison has also had a solid debut at the back.
1.17pmMissing Wolves striker Nouha Dicko has been speaking to Sky Sports News during the interval and he reveals that his hamstring injury isn't too bad, but will probably see him miss Tuesday night's trip to Ipswich Town.
46 minKICKOFF! Birmingham get the second half underway. No changes from either manager at the interval.
47 minHalf-hearted appeals for a penalty by the Birmingham players as Shinnie goes down in the area. It was a fair tackle by Ebanks-Landell and Taylor rightly waved away the appeals.
50 minWolves have started the second half just like they did the first - with plenty of the ball. It's all very controlled, but they're struggling to penetrate in the final third.
53 minIn all honesty, it's been a second half of poor quality from both sides. Wolves are neat enough on the ball, but seem to have no idea what to do when they approach the Birmingham area. As for the visitors, they struggle to keep the ball for more than three or four passes when they gain possession.
55 minCLOSE! Wolves have space in the final third for the first time. Henry's initial cross is blocked by the arm of Grounds, but Taylor and his linesman decide against giving a penalty. You could easily see that being given. Henry picks up the loose ball and his cross-cum-shot is palmed away from danger by Randolph.
56 minWOLVES SUBS: Jackett makes a double-change, taking off Jacobs and McAlinden for Sako and Edwards.
60 minExcellent goalkeeping by Randolph as he clutches Doherty's low cross to his belly. Clarke was right there and waiting to pounce on any kind of mistake by the Blues' keeper.
61 minSAVE! Superb stop by Ikeme to deny Grounds a goal from a corner. The ball dropped Robinson's way and you're expecting him to poke home, but a Wolves boot arrives just in time to clear the danger.
63 minBIRMINGHAM SUB: Arthur, who was bright in the first half, has quietened down and is now taken off for Brek Shea.
64 minThat change was made just after Wolves won a free kick on the right wing. Sako's delivery into the middle is cleared only as far as McDonald, whose low drive is well-hit but always curling wide.
66 minBIRMINGHAM SUB: Another change by the Blues as Shinnie is replaced by Callum Reilly.
66 minSAVE! Brilliant reactions by Randolph as he manages to tip over Edwards's header from close range after spilling Sako's fierce cross from the left straight to the other Wolves substitute.
69 minWith about a quarter of the game to go at Molineux, Wolves do look the more likely side to break the deadlock. Birmingham's best hopes of causing a shock will probably come from a set piece.
70 minHenry's near-post cross is flicked goalwards by Clarke, but he can't keep his header down under pressure from Morrison.
71 minOFF THE BAR! Edwards with an inventive chip that flicks off the top of the crossbar. It was neat hold-up play from Clarke before he fed the substitute, whose cheeky effort might have gone in had he directed it more towards the far post.
74 minThis afternoon's attendance at Molineux is 25,135 - the biggest gate of the season.
75 minCLOSE! Sako's wizardry on the wing is evident as he breezes by Caddis before firing a cross-shot that flies just wide of the far post and Clarke's attempt to nudge it home at the back stick.
76 minBOOKING! Clarke has been shown a yellow card, but I'm quite sure what for. I'm guessing he said something out of turn to referee Taylor.
77 minBIRMINGHAM SUB: Rowett changes his striker, replacing Donaldson with Thomas.
78 minWOLVES SUB: Moments after Davis dreadfully skies a half-chance for Birmingham, Wolves make their final change, also in attack, with Yannick Sagbo on for Clarke.
80 minWolves have plenty forward as Sagbo lays it off for McDonald, who should probably look for a teammate but instead shoots over the top.
81 minHenry with an inviting cross into the box that is met at the same time by Edwards and Morrison. Birmingham get the goal kick and the benefit of the doubt, much to Edwards's bemusement.
82 minA free kick in a great area for Birmingham is struck goalwards by Cotterill. It's way too close to Ikeme, though, and the Wolves keeper makes a comfortable save.
83 minBOOKING! A striker's challenge by Thomas and that earns him a yellow card. A bit harsh, but it was a nasty slide.
86 minInto the last five minutes of normal time then. Birmingham have silenced Wolves a little in the last five minutes or so and it's really hard to pick a winner. To be honest, a 0-0 draw would be about right. So much for my 3-2 prediction!
90 minCHANCE! That's as close as Wolves have come. Henry, who is my man of the match, almost nets the winner by firing towards the far corner. Randolph sticks out a leg to keep it out, but he can only divert it as far as Sako at the back post. It's a high bouncing ball and a tough chance that the hosts' top scorer can only blaze over.
90+1 minTHREE minutes are added on at Molineux. Can Birmingham hang on for an impressive point?
90+3 minWe're into the final minute now but we could play another couple because of an injury just suffered by Henry.
90+4 minBOOKING! Wolves go close again as Sako's shot is blocked. Taylor retrospectively books Caddis for an earlier pull on the Wolves winger.
2.11pmCome 7pm after Bournemouth's evening kickoff with Brighton & Hove Albion, Wolves could be down in fifth place if Derby, Watford, Bournemouth and Middlesbrough all win today.
2.12pmA point is enough for Birmingham to rise one place to 22nd. They'll definitely stay there, too, as Bolton played and were beaten last night by Norwich. As things stand, the Blues are just one point from safety.
2.14pmAnyway, time for us to say goodbye. Thanks for joining SM. Why not now click here to go to our live scores hub and pick a commentary for this afternoon. Enjoy!