It lifted Bilic's men up to 15th in the Premier League table with another home game against Hull City on the horizon on Saturday.
The Hammers went into the game just one place and one point off the bottom three so a win was all that mattered.
But here are five things we learned about West Ham from the game.
West Ham United's Winston Reid
1) Winston Reid and Pedro Obiang are fighting it out for top club honour
Ask any West Ham fan and they will tell you key centre back Winston Reid has been back to his imperious best in recent months.
The New Zealand skipper was brilliant yet again against Burnley and he needed to be as the Clarets bombared West Ham from all angles in the second half.
Reid looks a sure bet for the prestigious Hammer of the Year award this season but faces stiff competition from classy midfielder Pedro Obiang who has been equally as good in what has been a poor season for the team overall so far.
Both players were neck and neck shouts for man of the match against Burnley and if they continue in this kind of form it will be a tough choice for the club's fans come what May.
2) Bilic has got his buzz back
Slave Bilic has cut a somewhat forlorn figure this season, understandably given West Ham's precarious position in the table.
Pundits and supporters have been commenting on how downcast the popular boss has looked.
Skipper Mark Noble even told talkSPORT this week that his manager cannot be expected to be buzzing like he was last season.
But Bilic was as animated as ever on the sideline at the London Stadium, kicking and heading every ball as his side dug in for a hard earned victory.
It was a sight for sore eyes for Hammers fans and that spark is definitely back for the former Croatia boss.
West Ham's Dimitri Payet, Mark Noble and Andy Carroll celebrate
3) Carroll gives Payet room to breathe
Dimitri Payet has been a marked man this season and with good reason given his heroics for the Hammers last season and for France in the summer.
As a result the talismanic midfielder has not been effective as last season even if he has still been one of the club's best players this term.
West Ham made a mistake not bringing in another quality playmaker to take the pressure off Payet in the summer.
But big Andy Carroll does just that. Opposition defences can't afford to double and treble up on Payet with Carroll in the side as they usually have to employ a similar tactic against the former Liverpool man.
If Carroll can stay fit Payet will only get better and better.
4) Andre Ayew is finding his feet
Andre Ayew has endured a bit of a torrid start to his West Ham career since becoming the club's record £20.5 million signing in the summer.
Widely regarded as hugely overpriced the Ghana skipper spent the first four months of the season injured after tearing his thigh 30 minutes into his debut.
His appearances since coming back have been poor showings with many fans wondering just what Bilic and the Hammers board have seen in Payet's former Marseille teammate.
But his late cameo against Burnley should offer the Hammers hope as he looked a lot sharper and almost scored a wonderful solo goal which suggests there is plenty more to come.
5) Bilic must stop sacrificing Manuel Lanzini
Slaven Bilic complained that his side looked 'scared to win' in the second half.
But much of that is down to the manager who continues to withdraw midfielder Manuel Lanzini with around 20 minutes to go in matches.
Every time he takes the little Argentine playmaker off West Ham struggle in the transitions and have nobody in the centre of midfield who can run between the lines and carry the ball.
Therefore West Ham are always pressed back into their own half and it almost cost them again against Dyche's side who were on top after Lanzini went off.
Bilic must stop sacrificing his most gifted central midfield technician if he wants to close out games.