The home side then doubled their advantage a minute before the break as Downing's free kick found its way past Hugo Lloris.
Read Sports Mole's minute-by-minute report below to find out how all of the action unfolded between the London rivals at Upton Park.
11.45amHello there and welcome to Sports Mole's live text coverage of this afternoon's Premier League encounter as West Ham United welcome local rivals Tottenham Hotspur to Upton Park. We should have some team news through for you shortly...
11.47amIt may be the penultimate weekend of the season, but there is still plenty at stake for both of these teams. West Ham still aren't safe when it comes to avoiding the drop, while Spurs remain in the hunt for Europa League qualification.
11.53amTottenham boss Tim Sherwood has made just the one change to his starting lineup following last weekend's 1-0 win at Stoke City. Nacer Chadli misses out on a place in the squad as Gylfi Sigurdsson returns to the side. Sandro and Roberto Soldado are among the substitutes for the visitors.
11.56amWEST HAM SUBS: Jarvis, Armero, Vaz Te, Collins, Jaaskelainen, C Cole, Nocerino
11.58amWest Ham manager also makes one change after seeing his side lose 1-0 at West Bromwich Albion last weekend. Matt Taylor is recalled to the starting XI, while Matt Jarvis has to settle for a place on the bench.
12.01pmJust a point for West Ham this afternoon would see them secure their place in the Premier League for another season. However, if they fail to do that, they could seal their survival if Fulham and Norwich City both fail to win this weekend. The Hammers are all but there, though they will be well aware that this campaign has thrown up plenty of surprises.
12.04pmMeanwhile, Spurs will take a big step towards Europa League qualification if they earn a win at Upton Park. Tim Sherwood's side, who are currently in sixth place in the table, were forced out of the running for a Champions League place on Monday thanks to Arsenal's 3-0 victory over Newcastle United.
12.07pmWest Ham boss Sam Allardyce speaking with the club's official website: "We were one of the best clean sheets in the league eight or nine games ago and we haven't kept one since then. That's been our demise that has caused us a few problems.
"If we are to beat Tottenham it's no good to continue to play well if we carry on making basic errors. West Bromwich Albion's goal was down to our poor defending, not their ability and we have to eradicate that. We have to put the ball in the net when the chances come because otherwise the pressure heaps on you more than it should."
12.10pmTottenham manager Tim Sherwood speaking with the club's official website: "The players are aware, we've worked on defending crosses, winning second balls in the midfield and when we get the ball, we need to play our normal game. We need to break quickly and that's what we'll try to implement."
12.13pmOne notable inclusion in the Spurs squad today is youngster Alex Pritchard. The midfielder, who is 21 years old today, is named on the bench for the first time in a Premier League match. The last time that he featured in a Spurs first-team squad was for a Europa League fixture against PAOK in 2011.
12.22pmWest Ham looked destined for a top-half finish a couple of months ago following a run of four consecutive wins, but four defeats on the bounce has seen the team endure a poor string of results. There has been plenty of discontent around Upton Park in recent weeks, with some supporters letting Sam Allardyce know that they are not happy with the way their season is ending.
12.25pmMeanwhile, Spurs' patchy form has seen the North-London club miss out on Champions League football yet again. It's not all doom and gloom for Tim Sherwood's side though: reaching the Europa League will be considered as some kind of success. Right, Spurs fans?
12.28pmHEAD TO HEAD: Spurs have the superior record when it comes to past meetings between these teams, winning 53 matches compared to 43 for West Ham. There have also been 31 draws since they first faced each other way back in 1920.
12.31pmHowever, West Ham have had the upper hand in recent times, particularly this season. The Hammers recorded a surprising 3-0 win at White Hart Lane in the Premier League in October before beating their London rivals 2-1 at the Lane again in December in the League Cup. Can they make it a hat-trick this afternoon?
12.33pmWhile West Ham have beaten Spurs twice already this season, a Gareth Bale wonder goal separated the teams in this fixture last year as Spurs snatched the points in a 3-2 victory:
12.36pmPREDICTION TIME: This could well be a cagey affair this afternoon, especially considering that West Ham are not yet safe from relegation. Because of that, we here at Sports Mole can see these teams playing out a 1-1 draw. Just under 10 minutes to go until this one gets underway.
12.39pmOne stat that West Ham fans might not want to know is that, if the Hammers lose today, it will be the first time since 2011 that they have been defeated five times in a row in the top flight. You can thank the good folk at Opta for that...
12.42pmThe players are starting to emerge in the tunnel, which means that kickoff is not far away. It will be interesting to see if the West Ham fans turn on Sam Allardyce again this afternoon. It's fair to say that his position at the club is very much under threat. However, the same can be said of Tim Sherwood following widespread reports that current Ajax coach Frank de Boer is ready to take over at Spurs.
1 minKICKOFF! The teams are out, it's a gloriously sunny day in East London, and it will be Spurs to get us going in this local derby. Here we go!
1 minCHANCE! A dodgy moment inside the opening minute as Kane charges down a kick from Adrian, but the ball goes wide of the goal. That could have been a disastrous start for West Ham.
4 minThat opportunity for Kane aside, it's been a fairly even opening few minutes to this match. Not much in the way of flowing football, but there's plenty of bite in midfield as both teams look to gain possession. West Ham win themselves a corner, though Spurs manage to clear the danger following a bit of indecision inside their box.
5 minCHANCE! That would have been a lovely goal from a Spurs perspective. A lethal counter-attack involving Eriksen and Sigurdsson ended with Adebayor finding some space in the box, only for the striker to shoot straight at Adrian.
7 minOFF THE BAR! It's getting lively now! A West Ham corner caused some confusion in the Spurs box before Demel's looping effort hit the top of the crossbar. The ball looped up dangerously after that, but Lloris was able to collect.
10 minWest Ham are pressing Spurs really well at the moment. Sam Allardyce is sure to be pleased with the intensity that is players are showing. Meanwhile, Tim Sherwood is already looking a bit pensive down on the touchline.
13 minSpurs' liveliest player so far has been Kane. The young striker is doing a really good job of closing down Adrian when the West Ham goalkeeper is on the ball. Kane worried the shotstopper inside the opening minute and he's done so a couple of times since then.
15 minCHANCE! A decent opening for the visitors there as some patient build-up play ends with Paulinho heading straight at Adrian. The Brazilian should maybe have done a bit better there. West Ham go up the other end after that, but Downing can only shot high and wide from the edge of the area.
18 minYELLOW CARD! The first booking of the day goes the way of Spurs defender Kyle Naughton for a late challenge on Matt Taylor. The youngster gave referee Phil Dowd little choice there.
21 minIt's hard to tell who is on top at the moment. Both West Ham and Spurs are showing plenty of attacking intent, but that killer touch in the final third just isn't there. Still, it would be a big surprise if this game finishes goalless.
24 minSpurs are down to 10 men as Younes Kaboul is sent off for a foul on Downing! The West Ham winger broke free of the Spurs defence before being brought down by the defender on the edge of the box. It could be argued that Kaboul was not the last man, but Phil Dowd did not see it that way.
26 minHe may not have scored at Upton Park for a very long time, but Andy Carroll is back among the goals to give West Ham the lead! The striker saw his free kick tipped over the bar by Lloris, though there was nothing the Spurs keeper could do from the resulting corner as the big striker headed home via a deflection.
28 minSUBSTITUTION: Spurs boss Tim Sherwood makes a tactical change following that red card as Harry Kane is replaced by Vlad Chiriches.
31 minWest Ham are absolutely flying now. A deep cross from the right is almost met by Diame, but the midfielder just couldn't get his head to it. The hosts have done really well with their deliveries from wide positions so far, and Spurs are struggling to deal with it.
36 minSAVE! Oh, what a stop from Lloris! It was Taylor who launched a stinging half-volley towards goal from the edge of the box, but the Frenchman did brilliantly to get down low and push the ball away. Spurs are under tremendous pressure right now. They're really struggling to to get back into this match.
39 minWest Ham are bombarding the Spurs goal as we head towards the final five minutes of the half. It's not the prettiest football you're likely to see, though it has been very effective so far against the 10 men of Spurs. The visitors showed some menace early, only to tail off dramatically since going behind.
42 minWest Ham do double their lead before the break as Stewart Downing finds the net with a free kick from the edge of the box! Dawson was initially booked for a foul on Noble, which allowed Downing to step up from 20 yards and shoot past Lloris. Mind you, that was really poor defensive organisation from the visitors, with the ball seemingly going through the wall.
45 minThere will be two minutes of added time at the end of the half...
1.34pmPhil Dowd brings an end to what has been a great first half for West Ham, who lead 2-0 thanks to goals from Andy Carroll and Stewart Downing. In contrast, Spurs have been well below par. Their cause hasn't been helped by the sending off of Younes Kaboul, but, in truth, they rarely threatened before that.
1.37pmWhile West Ham's first goal is currently being credited to Carroll, it would not be a surprise to see it go down as an own goal from Harry Kane. The Spurs youngster, who was substituted after Kaboul's red card, diverted the striker's header into the net.
1.43pmSpurs might take some inspiration from the fact that they recently came from 0-3 down to earn a draw at West Brom, but it's hard to see how they're going to get back in this match. Apart from a couple of half-chances early on the visitors have not offered anything in an attacking sense.
1.46pmAs it stands West Ham will be securing their Premier League survival for another season. Meanwhile, Spurs' hopes of qualifying for the Europa League are under threat.
46 minSECOND HALF UNDERWAY! The teams are back out for the second half, and it will be West Ham to kick us off for the second half. No changes for either side at the break.
49 minIt's been a solid start to the half from Spurs as they look to pass the ball around and build up some possession. An early goal for the visitors could change the whole mood inside Upton Park because we know how antsy the West Ham fans can get.
50 minCHANCE! What a goal that would have been for West Ham as Diame hits an acrobatic overhead kick towards Lloris, but the Frenchman keeps it out with an instinctive save before the Spurs defence scrambel the ball awa.
53 minWest Ham are starting to build some momentum again now following that Diame effort. They're doing really well to win the ball back when they're out of possession and using it impressively when they get it.
55 minSAVE! What a stop from Lloris to keep his side in this match! Nolan got on the end of Carroll's knockdown, but the Spurs somehow got something on the midfielder's shot to get it away for a corner. The resulting kick saw Demel get a header towards goal, only to nod narrowly wide.
58 minWest Ham continue to pile on the pressure while Spurs struggle to keep them out. The hosts are still putting some excellent crosses into the box, though the visitors are just about doing enough to keep the score as it is. West Ham could easily have had a couple more goals to their name this afternoon.
61 minA moment of panic inside the West Ham box there as Adrian's fumbles a cross behind for a corner, which comes to nothing. The goalkeeper clattered into the post just as he caught Sigurdsson's cross.
64 minSUBSTITUTIONS: Spurs make a double substitution as Sandro and Roberto Soldado enter the action in place of Paulinho and Gylfi Sigurdsson.
69 minSpurs just cannot deal with the physicality of West Ham. Whenever the ball is in the visitors' penalty area, it looks like the home side might score. Carroll in particular is causing all sorts of problems.
70 minYELLOW CARD! Roberto Soldado goes into the book for chopping down Diame. The Spurs striker then raises his hands as both players get into a little scuffle afterwards. The Spaniard could well have been sent off there.
72 minSomething of a half-chance for Spurs as Soldado takes a great first touch in the box before shooting wide on the angle. That was born out of pure frustration. Still no sign of a genuine comeback from the visitors at the moment.
75 minFifteen minutes left to play at Upton Park, where West Ham still lead 2-0. It must be said that the Hammers have been excellent today following a run of four consecutive defeats. It was always unlikely that Sam Allardyce's side would be relegated considering how close it is at the bottom of the table, but it looks as if they are about to secure their survival in style.
81 minWest Ham are doing a good job of keeping the ball in the Spurs half as we enter the final 10 minutes of this match. Spurs are showing a bit of fight in terms of winning the ball back, though it's all come a bit too late.
83 minSUBSTITUTION: West Ham make a change now as Carlton Cole enters the field of play, replacing Andy Carroll. The big striker has been superb this afternoon for the Hammers.
86 minSUBSTITUTION: A final change for the home side sees Matt Jarvis come on for Kevin Nolan. Spurs midfielder Sandro was booked a few moments ago for a foul on Noble.
88 minNot long to go now, and it looks as if West Ham are going to be staying in the top flight for another season. It's been an up-and-down campaign for the Hammers, but they've done just about enough to get over the line. There can be no complaints that they deserve the points today.
90 minThere will be three minutes of added time...
90+1 minSAVE! Great stop from Adrian to deny Rose! The Spurs defender made a weaving run into the West Ham box before seeing his goal-bound effort tipped over by the goalkeeper.
2.38pmWest Ham make sure of their Premier League survival thanks to a comfortable 2-0 win at home to the 10 men of Tottenham Hotspur! A Harry Kane own goal and Stewart Downing's free kick in the first half were enough to seal the points for the Hammers following Younes Kaboul's red card. Meanwhile, Tottenham's chances of Europa League qualification now hang in the balance.
2.40pmThat's all from our live text coverage of this match, but don't forget that you can keep up to date with all of today's other fixtures in the Premier League right here on Sports Mole. Just follow this link here and see what takes your fancy. Goodbye!