Boro went ahead through Rudy Gestede's header in the first half and were almost dealt a late blow when Dael Fry seemingly turned into his own net during added time, only for the linesman to raise his flag for offside, allowing for the hosts to escape with all three points at the Riverside.
Relive all of the action with our minute-by-minute updates below.
5.07pmMonk's charges were beaten on the opening day following a hard-fought display from Wolverhampton Wanderers, while United enjoyed a welcome return to the Championship after edging past Brentford in their first game of the new campaign.
5.09pmBoro's league form has been a touch worrying this year, stretching back to their time in the Premier League last term. The Reds have lost their previous four league matches. The club has not lost five in a row since February 2013.
5.12pmSHEFFIELD UNITED SUBSTITUTES: Eastwood, Lundstram, Wright, Duffy, Lafferty, Evans, Brooks
5.15pmSo both sides find themselves at pretty much full strength, despite Boro recently allowing Marten De Roon to join Atalanta in Serie A. The hosts are operating with an impressive front three of Brit Assombalonga, Rude Gestede and Patrick Bamford. As for the visitors, United have opted for a four-four-two that sees both Billy Sharp and Leon Clarke lead their attacking line.
5.16pmBoro tend to have the upper hand when looking at the history between the two clubs. Monk's side have lost only two of their last 16 league games against the Blades. As things stand, Boro are also unbeaten in their last three matches against United.
5.18pmThe Blades have a decent defensive record at this ground, though, having conceded just once in their last two visits to the Riverside. That said, United failed to score in either of those games.
5.20pmBoro also hold a rather formidable defensive record when it comes to competing in the Championship. Middlesbrough actually have not conceded more than once in any of their previous 44 home games in the league, while also collecting 27 clean sheets in the process.
5.21pmOne man Boro will need to keep an eye on is the prolific Sharp in the Blades' attack. The frontman has bagged more goals than any other player in the top four tiers of English football since the beginning of last season. How is that for a stat!
5.23pmThe Blades also find themselves in a tidy spell of form in the league. United have now won eight consecutive league matches for the first time since the club was under the stewardship of Neil Warnock in 2005.
5.24pmPREDICTION! Just a couple of minutes to go now until kickoff at the Riverside and it is time to make a prediction. Middlesbrough were a tad unlucky on the opening day and I'm backing them to get off to winning ways back on home soil. United will likely make this hard for Monk's men, but I'm backing Boro to edge this 2-1.
5.27pmThe players emerge from the tunnel as we await the start of the contest. There is a great atmosphere inside the Riverside and this doesn't look too far off being a sell-out.
1 minKICKOFF! So the visitors get us moving here, kicking from left to right in a purple and white strip, while Boro feature in their typical home red.
2 minThere's a sense of competitive edge already in this encounter as Basham goes in on Forshaw and comes out the victor following a strong challenge. Not too much to report in the opening minutes as both sides try to find their feet.
3 minBoro seek to stretch the game already as Assombalonga breaks out wide on the right, with Bamford trying to pick him out with a ball over the top. Thankfully for United, Blackman reads the game well and is able to come out and gather without too much fuss.
6 minThe hosts have just started to get a grip of possession in midfield and are aiming to work out from there. The ball is soon moved to Christie down the right channel, although his cross into the middle is gathered comfortably by Blackman.
7 minCHANCE! The visitors should be ahead... A great piece of skill down the right channel sees Freedman break beyond the full-back and he then turns an almost-perfect ball into the centre of the box for Clarke. The striker stalls perfectly in the middle in order to receive the pass unmarked, but he can only fire an effort straight into an on-rushing defender.
10 minClever play from Forshaw draws a foul from Carruthers around 35 yards out from goal, giving Boro the chance to fashion a chance with 10 minutes played. Bamford has his sights on goal, although his shot from range balloons high and wide without troubling Blackman between the sticks.
13 minSome smart pressure on the right sees Christie win a throw, which United seem to make a meal of but eventually they clear. Boro can't find the required touch in the final third at the moment, but the hosts are certainly dominating possession.
16 minBamford gets on the ball having dropped deep in the right channel. He shows way too much talent for O'Connell, who can only bring him down in the ugliest of ways. The ball is soon fed forward into Assombalonga, who gets clattered fairly by Basham before being able to get his shot away on the edge of the box. Fantastic defending from the Blades man.
18 minFleck has been a bright spark for the visitors in midfield and has already made a few promising runs from the middle in the opening stages. This time he has the better of his marker, but he takes a heavy touch which allows Fry to intercept at the vital moment.
21 minGOAL! MIDDLESBROUGH 1-0 SHEFFIELD UNITED (RUDY GESTEDE)
22 minThe hosts have a lead and it arrives in a rather strange fashion. A ball into the box bounces up in the air with defenders scrambling to reach it. As is usually the case for Boro, Gestede times his jump perfectly to beat the away centre-backs and is able to loop a header up and over the reach of a stranded Blackman in order to give Boro the advantage.
25 minThat wasn't quite route one from the home side, but they have arguably been more effective using more direct methods so far in this match. Boro go long again and encourage Bamford to chase, leaving Stearman and Blackman to communicate well as the keeper comes out to kick clear under pressure.
26 minCHANCE! Boro work a set-piece nicely on the right flank and the ball is soon whipped towards the near-post. Gestede is alive to the delivery and almost gets his head to the ball, only for Freeman to leap in front of his man and deny the striker a clear head on goal.
27 minCLOSE! From the resulting corner, the ball is chipped towards the back-post, where Friend is allowed to move into the box unmarked. It looks as though he has an age to strike the ball towards goal, although his side-footed effort is a tame one and United clear with ease.
30 minThe long balls are working at the moment. This time Assombalonga and Bamford combine well after a long punt forward, until the latter takes a few too many touches and falls over his own feet inside the United box.
32 minThat goal appears to have settled some Boro nerves and the hosts are now moving the ball about with a touch more vigour. United yet to offer much in the final third and the home side are starting to look pretty good value for their lead.
36 minBoro fans will love Assombalonga come the end of today. The frontman puts in another decent piece of work as he chases down a seemingly lost cause, before forcing Blackman into kicking the ball out for a throw. Huge cheers ring out around the Riverside.
38 minCHANCE! Almost number two for the hosts and it's all down to a great cross from Christie. The winger swings a curling ball into the middle, where Gestede arrives late only to send his header just a few inches over the bar.
40 minThe one man you would want in that situation would be Gestede, but he put too much on that header. Any softer contact and that might have crept in. United will likely aim to simply hang in here as we approach the end of the first half. Boro are firmly on top now.
41 minForshaw wants to use the aerial capabilities of Gestede again and he stands a straight ball up into the middle of the box. Gestede has to react late and is almost able to get the required flick-on to test Blackman, but he misses the contact and the visitors have a goal kick.
43 minThe hosts are moving through the gears! Assombalonga shows standout awareness to turn and slip a ball into Bamford on the edge of the area. The frontman goes for glory with a curling effort from range, only to see his shot bend bend wide of the post.
45 minThe roles are reversed now as Bamford squares across the box for Assombalonga to shoot, but his shot is blocked in the centre and United can somehow scramble away the danger.
45+2 minHALF TIME: MIDDLESBROUGH 1-0 SHEFFIELD UNITED
6.19pmSo the referee brings an end to an entertaining half of football and Boro deserve their lead. Bamford has been brilliant so far this evening, especially in threading the midfield and attack. Gestede's goal proves the difference at the break, but the home side could maybe be two or three up by now.
6.21pmUnited have failed to offer much in the final third after a promising start, whereas Boro have really grown into a dominant position after taking the lead.
6.29pmUnited will need to bring Sharp into the game should they want to get anything out of this contest. The frontman has hardly had a sniff in the first half and is cutting a rather isolated figure in the Boro half.
45 minSECOND HALF! Boro get this moving again in the second period. Can United find a way back into this?
47 minSome shakiness at the back sees Friend needlessly give away a cheap corner in favour of the Blades. The ball into the middle is poor, however, leaving Randolph to claim comfortably off his line.
49 minChristie tries his luck from the edge of the box and is somehow able to earn a corner, despite a rather weak effort from the winger. The cross into the middle almost finds the towering Gestede, although the striker mistimes his jump and United escape unscathed.
51 minBoro appear to have settled into a similar rhythm from the first half and are now moving the ball around with confidence. Christie makes inroads once more down the right, leaving his cross to evade everyone in the middle of the away box.
53 minThe home side drop off for one of the first periods in the match and United are left with the chance to turn a cross into the box. Carruthers has the chance to deliver, but his cross is woeful and Randolph allows the ball to trickle out for a goal kick.
56 minSheffield United have managed to push their wing-backs slightly further up the pitch in the last few minutes and that has allowed them to push higher up the pitch too. The visitors have managed to wrestle back some share of the possession, although they do not quite have the required rhythm to break down the hosts.
60 minWe have 30 minutes to go and United have certainly improved in the second period. That said, they still find themselves behind a Boro side that appears to be threatening every time they move forward. This game is currently sitting on a knife-edge.
62 minSAVE! Stephens does so well on the right to find Clarke in the middle. The striker lays off the ball for Coutts on the edge of the area, who sees his speculative drive tipped beyond the post by a diving Randolph.
67 minSUBSTITUTIONS: Boro make a change then as Gestede is replaced by newcomer Lewis Baker, he recently signed on loan from Chelsea earlier this week. United also make a change as Ched Evans comes on to take the place of Sharp.
70 minBaker has his first chance to get involved when a cross is swung in from the right, although it's not the best of deliveries and Blackman can claim with two hands.
71 mnForshaw snatches possession in the middle of the park and begins to maraud forward, before laying the ball off for Assombalonga. The frontman has no chance, though, as he is surrounded by three defenders and is eventually hounded out despite his best attempts at fending them off.
74 minBoro pile forward and find themselves camped on the edge of the United box. Baker ends up losing his patience and tried to force the issue with a speculative ball that flies straight into the grateful grasp of Blackman.
77 minFreeman and Duffy try to work something cute on the edge of the Boro box and it almost comes off, only for the linesman to flag for offside. Replays show that the pair threaded that perfectly. Poor decision from the officials...
80 minSUBSTITUTION: Monk opts for another change now as 9Assombalonga is replaced by Ashley Fletcher. The frontman has had a great game today, especially with his pressing and running in behind.
84 minThe visitors are pushing with all that they have, which hasn't been too much in this game to be honest. Duffy makes decent progress down the right and is able to lump the ball towards the back-post. It looks as thought O'Connell might just get to it, but Friend does enough to put him off.
86 minStrong pressure from substitute Fletcher sees the youngster skip beyond the last man, although his cut-back across the box is soon thwarted by the retreating defence. Great movement from the former West Ham United man there...
89 minSAVE! United have a decent chance to put pressure on Randolph. The ball breaks to Clarke in the area and he drills hard down low towards the stopper's bottom corner, but the keeper responds well by getting down on two knees to block the shot.
90 minWe're going to have four minutes of additional time here at the Riverside...
90+2 minCHANCE! Some deft footwork from O'Connell earns United a cheap free kick off Christie. The ball is sent into the box where Fry seemingly heads into his own net. United wheel away in celebration, only to see the linesman somehow raise his flag for offside.
90+4 minFULL TIME: MIDDLESBROUGH 1-0 SHEFFIELD UNITED
7.24pmWhat a bizarre end to the game and it could be argued that United have been robbed of a point here. It seems as though the linesman has flagged for an offside on O'Connell, but replays suggests that the Blades man was just about on. Boro played well for large periods of the match, but found themselves under real pressure in the closing moments. That late disallowed goal will likely be talked about for weeks, but Middlesbrough will not mind as they now have a first win under their belt. Thanks for joining us today, that will be all from me!