The Browns are seeking their first 4-1 start since 1994 when they host the Colts, who have the NFL's best defense through four weeks, on Sunday.
An astonishing 49-38 win at the Dallas Cowboys last week, where Beckham had three total touchdowns, saw the team score their most points in a game since 2007.
In an impressive response since losing to the Baltimore Ravens in Week 1, they have had 34 or more points against the Cincinnati Bengals, Washington and Dallas, their best scoring streak since 1968.
IS BECKHAM BACK TO HIS BEST?
As Beckham struggled with a core muscle injury in 2019, he largely failed to meet high expectations in his first year after being traded from the New York Giants, finishing with 1,035 receiving yards.
The Cowboys win saw him produce his best display yet in a Browns jersey.
"You look at the games that we won, and it was not like it was a fluke," Beckham told reporters about the Browns' start to 2020.
"I’ve just been waiting," he added of his breakout game against Dallas, where he had 81 yards through the air and 73 on the ground.
"I know what I can do. I know what I am capable of. Just trying to find ways to keep this train rolling. This is probably one of the best spots I have been in.
"I had to really strain heavy last year - I did not want to run any faster than I needed to. I am definitely stronger, faster this year than I was last year. I am just all around healthier."
The Colts represent stiff opposition. They also struggled in a poor opener, losing to the Jacksonville Jaguars, only to respond with wins over the Minnesota Vikings, New York Jets and Chicago Bears to also sit 3-1.
With star running back Nick Chubb out injured, Jarvis Landry believes his close friend and team-mate Beckham will have to produce more fireworks, after his spectacular 50-yard touchdown run on a reverse settled the game with Dallas.
"Greatness - listen, I have not seen plays like that in the NFL in a long time," said fellow wide receiver Landry, who had earlier thrown a TD pass to Beckham.
"Only special guys make those type of plays. He is very special. That is something that we are going to continue to need out of him for the rest of the season.
"Last year, he was dealing with a major injury that obviously he had to have surgery and coming into a new system, a new team and all of these things, I think that that weighs on anybody."
HISTORIC NUMBERS FOR COLTS DEFENSE
The Colts defense ranks first in the NFL for points allowed per game (14), yards per game (236.3) and yards per play (4.4).
The 945 total yards allowed is the best Colts figure through the first quarter of a season since 1971, per Stats Perform data.
They have also had the Browns' number over recent years, winning eight of the last nine meetings and five straight in Cleveland. However, each of the last 10 games have been decided by eight or fewer points.
For the Browns, defensive end Myles Garrett has had a spectacular start to 2020 and his 31 pressures are second to only to the Bears' Khalil Mack.
That form has helped the Browns generate turnovers – they have forced 10 fumbles and recovered six of them, the first team to have had such a streak since the 2015 Detroit Lions.
But they have also allowed as many touchdowns as their offense has scored (16) and given up 63 passing plays of 10 or more yards, a record which is second-worst in the league (the Seattle Seahawks have allowed 74).
MILESTONE FOR RIVERS
Pressure may be harder to come by this week, as Colts QB Philip Rivers has only been sacked three times behind quality offensive line play he was not used to with the Los Angeles (formerly San Diego) Chargers.
Rivers will almost certainly become the fifth player in history to reach 5,000 career pass completions, following in the footsteps of an elite group – Drew Brees, Tom Brady, Brett Favre and Peyton Manning. He goes into the game with 4,996 to his name.
Colts coach Frank Reich has been thrilled with Rivers, even though the Colts' run game and stellar defense meant he only had to throw for 190 yards in last week's win over the Bears.
Reich said: "He made some huge plays on third down trusting his receivers, the throw to T.Y. Hilton, the throw to Marcus [Johnson] down the field - we get the pass interference.
"We had the other one that we missed to T.Y. down there. I know Philip said something about that missed throw. There was a little collision down the field that kind of precipitated that."
And Hilton is not worried about having just 13 catches (162 yards, 22 targets) through four games, so long as the Colts keep winning.
He said: "I have got no problem with what’s going on - we are winning and I am having fun.
"I can only control what I can control and when the ball comes my way, I'll be ready. Whatever my team needs, I'm always there to make a play."
