The left back scored the match's only goal at Upton Park.
In Saturday's meeting of two of the Premier League's form sides, Newcastle was searching for its seventh straight triumph in all competitions.
Yet it was undone by a West Ham team that has now picked up 13 points from its last five home games, with left back Cresswell proving the matchwinner.
The 24-year-old – who joined West Ham from Championship side Ipswich Town in July – settled the encounter with a close-range strike in the 56th minute as Alan Pardew's defense was breached for the first time this month.
In a game of few clear-cut opportunities, Newcastle could not find the goalscoring touch and its frustration was compounded when midfielder Moussa Sissoko was sent off for picking up two yellow cards in less than a minute.
West Ham's sixth league win of the campaign sees it leapfrog Newcastle in the table.
The visitors made a bright start to proceedings and went close inside the first three minutes as the in-form Ayoze Perez shot wide of the far post following good work down the right from Yoan Gouffran.
Stewart Downing returned from injury for West Ham as one of three changes by Sam Allardyce and was the first to test Newcastle goalkeeper Rob Elliot, who was named in the starting XI – along with Gouffran and captain Cheick Tiote – due to a twisted ankle sustained by first-choice shot-stopper Tim Krul in training.
Perez was the most dangerous player on the pitch in a dour first half and provided another example of his attacking threat by cleverly flicking into the side netting after a near-post cross from Sammy Ameobi, who then curled wastefully wide in the 44th minute.
Elliot could do nothing to prevent Cresswell from putting West Ham ahead.
The left back capitalized on some sloppy Newcastle defending, latching on to a mis-hit shot from Cheikhou Kouyate and slotting into the bottom-left corner from close range.
Pardew threw on Papiss Cisse and Remy Cabella in response to falling behind, yet the changes had little impact for a Newcastle side that labored in search of an equalizer.
And a disappointing afternoon for Pardew's men worsened courtesy of two moments of madness from Sissoko, the France international seeing red for a late challenge on former Newcastle striker Andy Carroll less than 30 seconds after being cautioned for kicking the ball away.
Sissoko's early exit effectively ended any hope of a Newcastle fightback and leaves an already injury-hit side facing further problems ahead of Tuesday's visit to Burnley.