The Hammers claimed a fourth straight Championship victory, and a fourth on the road, as Tony Mowbray's Boro lost for the first time at the Riverside this season.
A home record stretching back to February last year came undone as Piquionne nodded Mark Noble's cross home with nine minutes played.
West Ham dominated throughout and, despite a spirited second-half performance from their opponents, Cole took advantage of a late Matthew Bates error to slot in a second.
Sam Allardyce had promised to shake up his team, and did so, making four changes at the Riverside.
Ivory Coast international Guy Demel made his debut, with Piquionne, Matt Taylor and Papa Bouba Diop also included.
Boro drafted in Merouane Zemmama for the injured Barry Robson.
Tony Mowbray had intended to give the visitors an uncomfortable night on Teesside, but Allardyce's men looked the more assured side for most of the first half.
Taylor forced Jason Steele to parry clumsily with his dipping free-kick as the match sparked into life.
The hosts laboured to recover the ball as the Hammers set up camp, and within nine minutes their poor retention had cost them dearly.
Nicky Bailey dithered in possession in his own half, only for Noble to ghost in and supply a killer cross for Piquionne to nod home.
With seven league goals to his name going into this encounter, Marvin Emnes was repeatedly forced out onto the flanks by the wary Hammers defence.
But in the 26th minute, he turned this to his advantage, whipping in a cross which Faris Haroun might have tucked away with a better connection.
Scott McDonald then weaved in from the right wing to alarm Rob Green with a snapshot that the former Norwich stopper could only bundle away for a corner.
Their renewed vigour afforded Boro the best opportunities before the break, Zemmama given time and space to blast narrowly above the target, with Emnes forcing a stunning fingertip save from Green as he cut in once more from the left.
West Ham led the Championship table at the half-time interval by merit of Southampton's losing position at home to Hull.
Perhaps softened by reports from St Mary's, Allardyce's charges relaxed their complete dominance as the second half began.
Haroun was unlucky to fire wide after Joe Bennett had sent a dangerous ball into the penalty box.
And on the hour mark, Rhys Williams glanced Tony McMahon's cross carelessly off target with the goal gaping.
The spectre of Boro's last meeting with the east London side arrived as Cole was introduced for Piquionne with 20 minutes remaining.
Cole was among the scorers as the north east club bowed out of the Premier League with a 2-1 defeat at Upton Park in May 2009.
Iron skipper Kevin Nolan, making his 400th career league appearance, marshalled his midfield superbly as Boro grew in confidence and began to run into channels towards the final whistle.
And Mowbray's side finally waved goodbye to their excellent record as Cole seized on the loose ball exposed by Bates' slip to round Steele and pass into the net.
But with the Saints recovering to beat Hull, the quest for top spot continued for Allardyce and his fluent Hammers outfit.