The striker found the net from close range to round off a dominant display for Newcastle, who were playing their first game since the Premier League restart.
Sheffield United did not create many opportunities at St James' Park and were reduced to 10 men early in the second half when defender John Egan collected his second yellow card.
Egan, who was cautioned for clashing with Joelinton over an offside decision in the first half, brought down the striker to receive his marching orders from referee David Coote.
Ritchie doubled Newcastle's lead in the 69th minute with a swerving shot from the edge of the box, before Joelinton recorded only his second league goal of the campaign.
The result means Chris Wilder's Sheffield United, who played out a goalless draw against Aston Villa in their first match back, remain seventh in the standings and four points behind fourth-placed Chelsea.
Meanwhile, Newcastle moved up to 12th spot with 38 points to surely put any remaining relegation fears to rest.