Their 10th top-flight win avenged losing at Selhurst Park 4-1 in November.
Leeds climbed into the English Premier League top 10 after beating Crystal Palace 2-0 on Monday.
Jack Harrison's deflected shot gave the home side a flying start, and Patrick Bamford tucked home a rebound for his 12th league goal and 100th of his career early in the second period.
“After being out of the league for 16 years it is important for a club like Leeds to get a footing and build from that,” Bamford said. “This is no more than we've deserved. It bodes well for the future of Leeds.”
Their 10th top-flight win avenged losing at Selhurst Park 4-1 in November.
It should have won by more and registered a first clean sheet in seven matches this year.
Palace arrived in freezing West Yorkshire riding two straight league wins but was a clear second best for most of the match. The London side lacked a cutting edge in the absence of injured top scorer Wilfried Zaha.
“We were not able to pressurize them like they pressurized us,” Palace manager Roy Hodgson said. “We are a passing team and when we don't pass the ball well we fall below our standards.”
Leeds was quick to punish Palace for allowing too much space on the edge of the penalty area when Harrison's well-struck shot deflected in off Gary Cahill in the third minute.
Leeds made another fast start to the second half. Raphinha's thumping shot was well saved by goalkeeper Vicente Guaita and Bamford followed up to turn home the rebound from eight yards.
