The midfielder finished from close range in the 47th minute after Palace goalkeeper Vicente Guaita could only tip away a Luke Freeman effort into the box.
United, back in the top flight for the first time in 12 years, drew 1-1 at Bournemouth on the opening weekend.
Palace have yet to score a goal this season, having started with a 0-0 home draw against Everton. Re-live the live action below.
It's been a while since Sheffield United's last home game in the Premier League. In that time Phil Jagielka left the club, played 385 games for Everton and then returned.
They also spent six years in League One. It's been a long journey back to the top league in English football and the home fans will relish every minute of today's game.
Today's match is the first meeting between the sides for eight years, and the first in the Premier League since its inaugural season back in 1992-93.
The last time these sides met at Bramall Lane, there were five goals, three penalties and two red cards with the Blades scoring twice in the last five minutes to win 3-2.
Sheffield United are on a seriously good run of form. They've lost just one game in their last 19, albeit the majority of those games came in the Championship last year.
Since Chris Wilder was appointed manager, United have earned 259 league points, only Luton and Manchester City have earned more in that time.
Going against them today is their Premier League record on Sundays. They've played five games on Sundays and haven't won one. Drawing four and losing one.
Crystal Palace play well away from home. Their record last year was the sixth best in the Premier League.
They won five of their last six away fixtures including the final three of the season. However they've never won four consecutive away matches in the top flight.
Starting up front today for Palace is Wilfried Zaha. He scored 10 Premier League goals last season, nine of which came away from home.
Roy Hodgson has done well since taking over at Crystal Palace but he still thinks his team has a ways to go.
"We think there are more goals in the team than we were able to show last year - it's up to our front players and goalscorers to show that.
"I think as the season wore on we became better at scoring goals and taking our chances and I'm hoping that is going to continue and get even better this season."
We could be in for an entertaining match, especially with Sheffield United's 'overlapping centre-backs'.
They played in a 3-5-2 against Bournemouth - the three centre-backs working alongside wing-backs.
The two widest of the central defenders (in this case, number 6, who is Chris Basham and 5, Jack O'Connell), are given the freedom to run around their full-backs, essentially creating another wing-back role on each side.
Kick off: Here we go, Sheffield United's first home Premier League match in years. They start the match going forward down the left wing before Townsend clears the ball away.
3 mins: Jack O'Connell gets a knock in the head and goes to ground. He's seen to by the medical staff as is the procedure these days with any type of head injury. He looks to be okay.
6 mins: Benteke gets the first effort on goal for Crystal Palace. Sheffield United lose the ball in the middle of the park and a long ball forward is brought down by Zaha. He plays the ball into Benteke to the right side of the box, O'Connell loses the man and Henderson is forced to make the save as the shot comes in.
15 mins: Lundstram fires off the first shot for Sheffield United. Some good overlapping play from O'Connell wins the ball back on the left wing, he passes it inside to Lundstram who fancies it, he shoots from a long way out and sends the ball wide of goal.
Sheffield United vs Crystal Palace kicks off at 2pm.
Where can I watch it?
The match will be shown live on Sky Sports Main Event and Sky Sports Premier League from 1pm. Highlights will be shown on Match of the Day 2 on BBC One at 10:30pm.
