Plenty of people had written off Bournemouth's chances of staying in the top flight three months ago when they suffered four league defeats on the trot, but since then, they have managed to claim three victories, four draws and recorded just one loss.
At the moment, Howe's team reside 16th in the table, four points above relegation, and a victory tomorrow night could move them above 14th-placed Chelsea for 24 hours at least.
Last August, the Cherries entered the Premier League for the first time in the club's history promising attacking, free-flowing football and an adamance from Howe that he would not adapt his style for his opponents.
They were knocked by long-term injuries to Tyrone Mings, Max Gradel, Callum Wilson and Tommy Elphick and went on a downward spiral, losing to Manchester City, Tottenham Hotspur, Southampton and Newcastle United across October and November.
In December, when games come thick and fast, Bournemouth had a positive run, sealing victories over Chelsea, Manchester United and West Bromwich Albion, and the only blip in their last eight league games is a 2-0 defeat to league leaders Arsenal.
Added to their positive results, the South Coast side have also been quick in the January transfer market by snapping up Juan Iturbe on a six-month loan from Roma and Benik Afobe from Wolverhampton Wanderers in a permanent deal thought to be worth in the region of £10m.
Despite the uncertainty surrounding their long-term position in the Premier League, Howe and the club's board are able to attract decent targets, who could play a big part in the Cherries' survival fight.
Bournemouth's problem this season has been conceding goals and they have allowed 34 to get shipped past them already, but they have been a lot more sturdy at the back of late having let in just two in their last three top-flight fixtures.
Recent form: WWWDLD
Recent form (all competitions): WWDLDW
West Ham United
Slaven Bilic's side have proven that they can more than hold their own away from home as they have already administered wins over Arsenal, Liverpool, Manchester City and Crystal Palace this season.
The London club are on a three-game winning run following Saturday's 1-0 victory over Championship side Wolverhampton Wanderers in the third round of the FA Cup, although all three of those triumphs have come at Upton Park.
The Hammers have not lost any of their last seven games in the top flight and in 20 fixtures, they have only suffered defeat four times, suggesting that they head into Tuesday night's contest as favourites for an away win.
The team will be particularly boosted by their 2-0 win over Liverpool last week as they were comfortable winners, and Andy Carroll managed to get one over his former club by adding to the scoreline in the second half following Michail Antonio's 10-minute goal.
Carroll has worked his way back into contention at Upton Park following his lengthy spell on the sidelines with injuries, and he has paid back Bilic's faith by scoring in the team's last two league triumphs.
There have been questions over the striker's long-term future at West Ham, but Bilic recently told reporters: "We never said we were willing to sell Andy, not me, not the chairman. He's a very popular player. We do not want to sell him. I think he likes it here, he's very important in the dressing room. I know he is happy here."
West Ham have the chance to move within one point of fourth spot if they earn a victory tomorrow night, but in their last four league games on the road, they have come away with a draw.
Recent form: DDDDWW
Recent form (all competitions): DDDWWW
New signing Afobe could make his debut for Bournemouth following his transfer from Wolves at the weekend, but the striker could be a substitute to begin with as he only arrived at the club a matter of days ago.
As for West Ham, Dimitri Payet could make his first start since November after recovering from an ankle injury. The midfielder has been named on the bench in the Hammers' last two games, but is in line to be in the first XI on Tuesday night.
Bournemouth possible starting lineup:
Boruc; Daniels, Cook, Francis, Smith; Surman; Stanislas, Gosling, Arter, Ritchie; Murray
West Ham United possible starting lineup:
Adrian; Cresswell, Ogbonna, Collins, Jenkinson; Payet, Kouyate, Noble, Antonio; Carroll, Valencia
Head To Head
Overall, though, West Ham have the edge having sealed three victories in their last five meetings, but those matches span between 1929 and 2015.
Prior to this season, the two sides met in the League Cup in 1999, and it was the Hammers who progressed by grabbing a 2-0 win on home turf.
We say: Bournemouth 1-2 West Ham United
Both sides are in decent form, and while Bournemouth have the home advantage, West Ham have proven that they can get the points that they need on away soil. In addition to that, Bilic's side have only lost two of their last 15 fixtures in all competitions, while Bournemouth have drawn four and lost three of their nine Premier League games at home. It could be a tight game, with just one goal edging it, but West Ham should just have enough to take all three points.