Howe, who is under scrutiny for the first time in more than four successful years in charge at St James' Park, watched his side end a run of three consecutive league matches without a win.
The result provided much-needed breathing space, even if it did little to disguise ongoing concerns, with Newcastle still sitting in the bottom half of the table.
The visitors appeared in control for long spells but were forced to survive a strong second-half comeback attempt from Burnley.
Newcastle goalkeeper Nick Pope proved decisive, producing a series of crucial saves to preserve the lead and ensure the points were secured. His contribution was central to a win that could have slipped away as Burnley pushed aggressively after the break.
Despite the victory, the broader league context remains challenging. Newcastle are four points behind fifth-placed Chelsea and face a demanding run as they attempt to climb the standings.
Their upcoming schedule offers an opportunity to build momentum, with two consecutive home matches before travelling to face Wolverhampton Wanderers, who currently sit bottom of the table.
"We're in there fighting and scrapping for every point in the Premier League," said Howe.
"It's been a difficult season and hasn't been plain sailing but the points gap is minimal if we can put a run together. It's a big if. It's that magic word, consistency, being able to back up results which has been our failing.
"That's what we're looking to do and if we can things can change quickly, the perspective is different. We haven't been able to do it yet and we're running out of opportunities. Beyond this, I don't think we'll get another chance."
Newcastle head coach Eddie Howe has firmly ruled out any move to Manchester United, reaffirming his contentment at St James' Park despite speculation linking him with the Old Trafford vacancy following Ruben Amorim's departure.
Pascal Gross described his return to Brighton as "incredibly emotional" after making his second debut in the Seagulls' 2-0 Premier League win over Burnley on Saturday.
Newcastle United manager Eddie Howe praised his side's resilience after guiding the Magpies to a 3-1 victory over Burnley at Turf Moor on Tuesday.
Kaizer Chiefs right-back Thabiso Monyane has opened up on his close bond with Burnley striker Lyle Foster, revealing why he once lived with the Foster family and considers the forward his brother.
