Striker Smith then added his second and the home side's fourth in the closing stages to seal the victory.
You can find out how the match unfolded with Sports Mole's minute-by-minute updates below.
12.48pmAfternoon all. There is no early Premier League fixture today, so our focus turns to Elland Road where Leeds United welcome Birmingham City. It's still early days, but if either side wants to be challenging towards the top end of the table, it's a game that both could do with winning. Let's hope that it makes for a good contest.
12.50pmNow, without further ado, let's turn our attention to the starting lineups. Next up is how the hosts will begin this fixture...
12.53pmSo, Brian McDermott has opted to make four changes to his side today. Scott Wootton, Matt Smith, Luke Murphy and Samuel Byram have all been restored in place of Lee Peltier, Michael Tonge, Paul Green and Noel Hunt. Meanwhile, the controversial El-Hadji Diouf misses out altogether.
12.57pmLee Clark has gone one better than his opposite number McDermott by making five alterations to his starting lineup. Kyle Bartley, Lee Novak, Paul Caddis, Oliver Lee and Wade Elliott all start, while Manchester United loanee Jesse Lingard will continue in an attacking role.
12.59pmWhile we are here, let's take a quick look at who has been named among the substitutes as well...
1.04pmSo, who is the favourite between two teams that have been consistently inconsistent this season?! Well, if recent history is anything to go by, the smart money would go on Birmingham, despite the fact that they are playing away from home. They've won the last five meetings between the two sides, including two at Elland Road.
1.08pmThe away side can also take some confidence from the home team's recent performances. Out of their last seven Championship fixtures, Leeds have lost five of them. Having said that, the Blues have won the same amount of matches during that time period (two), but they have picked up an extra draw. This one really is so difficult to call!
1.13pmAs the players head on to the pitch, here is what both managers have just said to Sky Sports News.
MCDERMOTT: "We've done a lot of work in training over the last two weeks. We are here now and looking forward to the game. We need a real fast start and to get the crowd into this game."
CLARK: "We want the players to go out and express themselves and score goals. We've got to be a threat in the final third. We need to handle the intimidating atmosphere."
1 minGAME ON! Visiting Birmingham, who will be attacking from right to left during the first half, get this encounter off and running.
4 minFirst run forward from Leeds full-back Byram and it appears that he is going to get a shot at goal. However, at the last second, Birmingham defender Dan Burn gets across with a sliding challenge to halt Byram's run. Nevertheless, it's a big positive for the home side to have their young defender available again following a hip problem.
7 minA painful moment for both Leeds midfielder Rodolph Austin and veteran Birmingham defender Paul Robinson. The pair collide in mid-air, with the latter having to leave the field for a couple of minutes to receive treatment for a cut. A proper challenge! Neither of them was going to pull out of that one!
9 minSAVE! Burn is bound to be the most relieved man inside Elland Road right now. His mistake gifts possession to Ross McCormack, who has just Darren Randolph to beat. The Birmingham goalkeeper makes amends for his teammate, though, and blocks the striker's low effort. Leeds are starting to turn the screw.
11 minCHANCE! Jason Pearce may have been under some pressure, but he really should have put Leeds in front. The centre-back meets a corner with a powerful header, but from six yards out he heads the ball way over the target. That's not one that he will look back on too fondly.
13 minSAVE! Randolph could well be in for a busy afternoon. Once again he is called into action to deny McCormack from a narrow angle after he was picked out by a brilliant low bass from Randolph on the right. At this rate, it will only be a matter of time before Leeds break the deadlock here.
17 minAnother half chance for McCormack, who this time is denied by Caddis. As the ball floats over the top of the Birmingham defence, it appears that the Leeds frontman has a clear volley at goal. Scottish utility man Caddis retreats just in time, though, to snuff out the danger.
18 minYou can't keep getting away with giving McCormack chances. Randolph rushes off his line and gets to the ball ahead of Leeds striker Matt Smith. His touch is far too heavy, though, and Austin gains possession. He in turn picks out McCormack, who lifts the ball over a stranded Randolph and into an unguarded net from 25 yards out. An awful goal for Birmingham to concede, but a deserved one as far as Leeds are concerned.
22 minDISALLOWED GOAL! It would have been an instant response from Birmingham but for the linesman's flag. Chris Burke's shot from the edge area breaks off the Leeds defence for Novak, who rolls the ball underneath Paddy Kenny and into the net. He's given offside and replays show that it was the correct decision from the referee's assistant.
26 minCHANCE! Austin has just provided any youngsters watching with a real lesson on how not to shoot! McCormack again is in the thick of the action, having beaten three Birmingham defenders before playing in his Jamaican teammate. He goes for an instant shot, which goes closer to hitting the corner flag than the back of the net!
29 minCHANCES! Some great defending from Stephen Warnock just now has surely stopped Birmingham from levelling up proceedings. David Murphy sends over a teasing free kick from the right flank, which Novak looks certain to head in. At the last moment, though, Warnock rises highest to head over the bar. Then, from the resultant corner, Burke passes up a good opportunity when he fires wide from the edge of the area.
31 minMcCormack is incensed at what he believes was a foul from Burn as he went through on goal. Replays show that he was indeed pulled back by the Birmingham defender, but that is difficult for the referee to spot.
33 minWe may only be 33 minutes in, but I'm tempted to say that it's game over here. McCormack once again is at the centre of it, having collected possession on the left wing. He then picks his head up and sends the ball into the area for an unmarked Austin, who has the simple task of heading into the net from six yards out. It's long a way back for the Blues now.
38 minSince the second goal, Birmingham have had quite a bit of the ball but they don't really look like creating too much. It's vitally important that they don't concede again before the break, while a goal for themselves certainly wouldn't hurt their cause.
42 minIt's now Leeds who are back in the ascendancy and it must be said that the partnership between McCormack and Smith is starting to show signs of flourishing. As a duo, they are not too dissimilar to Kevin Phillips and Niall Quinn, who had a lot of success in front of goal at Sunderland in the later 1990s and early 2000s.
45 minMcCormack was always going to be involved in the third goal, wasn't he?! He collects Smith's flick on and then fires the ball goalwards. Randolph gets it clear with his boot, but only as far as Smith, who wrong-foots the visiting goalkeeper with his rebound effort. The big centre-forward deserves that because like his striker partner McCormack, he's caused problems throughout the half. Meanwhile, there will be two minutes of stoppage time.
2.05pmWell, whatever McDermott did in training with his players during the international break, it's worked! They were rampant during that 45 minutes and deserve to be so far in front. In fact, it's the first time that they have scored three goals in a game since December 2012.
2.08pmBut where an earth do Birmingham go from here? Realistically they are not going to take anything from this game, so it's all about regaining some pride. Clark is bound to be fuming with his players, but the best he can hope for really is that they don't lose the second half.
2.11pmHaving just had a quick glance at the Birmingham bench, perhaps bringing on the likes of Shane Ferguson and Andrew Shinnie could swing the game their favour. The pair are lively wingers who will look to take the game to their opposing full-backs. Then there is Nikola Zigic. Granted he has not set the world alight since joining the Blues, but Novak has been relatively quiet so far.
2.15pmFrom the home team's point of view, McDermott is likely to demand more of the same. It's unusual that a team in such control comes out for the second half and replicates the same performance - the foot more often than not comes off the gas somewhat. However, Birmingham have been that poor at the back that Leeds may not be able to fail but score more goals!
46 minSECOND HALF UNDERWAY! As I predicted, Clark has made changes at the break - two of them in fact. Zigic and Shinnie enter the action in place of Burn and Novak as Leeds get the second half started.
49 minCHANCE! That's much more positive from Birmingham as their two substitutes link well. It's Zigic who threads a pass through for Shinnie to start the move. The Scot then takes one touch, before attempting to curl a low shot into the bottom corner. Kenny in the Leeds goal doesn't move, but the ball slides inches wide of the target.
54 minThe second half has actually started just how you would have expected it to. Birmingham have seen much more of the ball, while Leeds seem content to defend what they have. It's got to be said, it's not making for a great spectacle. A goal for the away side could well change that, though.
58 minBOOKING! The first yellow card of the contest and it goes to Leeds full-back Warnock. The former Liverpool player can have no complaints either because he wipes up Elliott as the Birmingham winger looks to move into the final third of the pitch. I think that is what is known as 'taking one for the team.'
61 minSAVE! The home side should really be celebrating their fourth goal of the afternoon. Teenager Alex Mowatt frees Austin, who bursts through on goal. He's met by Randolph, who spreads his body well to deny the Leeds skipper his second goal. Moments later Birmingham's Kyle Bartley goes into the book for a foul on McCormack.
65 minSAVE! Fantastic defending from Leeds's Tom Lees, who reacts quickly after Elliott's wayward cross beats Kenny. The ball is about to loop into the net, but the Leeds defender retreats just in time to clear the danger. Moments later, Zigic's powerful strike from distance is tipped away by Kenny.
69 minOFF THE POST! It really isn't Birmingham's day. It seems that Murphy does everything right with his free kick from 25 yards which has Kenny beaten all ends up. At the final moment, though, the ball cannons off the upright and is hacked clear to safety.
72 minSAVE! Fair play to Birmingham because they are continuing to knock on the door. This time it's Burke who tries his luck from the edge of the area, but Kenny gets down in time to stick out a hand and turn the ball around the post. It may have come far too late, but at least Birmingham have put up a fight in this half.
73 minSAVE! That is perhaps the best save you will this weekend from Randolph. Smith does absolutely everything right as he plants a cross from McCormack towards the top right-hand corner of the net. Somehow, though, Randolph throws himself towards the ball is able to tip clear the danger.
74 minThis time Randolph had no chance - in fact had he got anything on the ball, he would probably have gone into the net with it! Austin picks out Mowatt, who in turn crosses into the area from the left. It's meant for an onrushing Smith and he powers a headed effort into the roof of the net. It's an unstoppable header and is Smith's third Championship goal of the campaign.
79 minLeeds are now in complete cruise control, while Birmingham look like they just want the game to end. They looked interested for a time, even at 3-0 down and to be fair they were actually carving out some chances. Since the fourth goal, though, the stuffing has been knocked out of them.
84 minBurke has just summed up the whole afternoon as far as Birmingham are concerned. Having just wriggled himself free on the right flank, he has the chance to cross into the area, where six of his teammates are waiting. There's far too much power on his delivery, though, and the ball flies out for a goal kick.
88 min'Sacked in the morning' is the chant around Elland Road right now. It's being aimed at Clark, who has the camera pans to him, looks a man with the weight of the world on his shoulders. It will be interesting to see if the Birmingham board react to this defeat over the coming days.
90 minSUBSTITUTION: First change of the match for Leeds and it's the skipper Austin, who goes off to a massive round of applause from the home faithful. He's been replaced by veteran midfielder Michael Brown. Meanwhile, at least three minutes of stoppage time will be played.
3.10pmSo, there you have it - it's a resounding victory for the home team, who have ended a poor run of recent form. They can now look upwards over the coming weeks. In contrast, Birmingham must have a bit of a sinking feeling - they were hammered today if truth be told.
3.12pmThat's all we have time for from Elland Road. Thanks for joining us this afternoon. Until next time, goodbye.