The star signal-caller agreed to a four-year, $240 million contract extension on Sunday morning -- just before Dallas took on Cleveland in its season-opener -- and when TMZ Sports talked with Drew about the record-setting deal ... he told us the QB is deserving of it all.

"Look at the quarterbacks around the league," Pearson said. "Teams are struggling to find good quarterbacks. They're looking down the depth chart to see who's available."

Of course, there were haters all over social media who disagreed ... pointing to Dak's 2-5 playoff record as the No. 1 reason he shouldn't have gotten the big money.

However, Pearson said Prescott's exactly the kind of leader Dallas needs -- comparing the 31-year-old to Roger Staubach, Troy Aikman and even Tony Romo.

"He says all the right things," Pearson said, "and he says those things because he believes it."

So far, the deal's looked pretty good ... as Prescott played well in a 33-17 blowout win over the Browns.

He won't have to wait long to keep proving it -- the Cowboys play next this Sunday at home against the Saints -- and Drew says the offense is going to have to score a bunch to get to 2-0.

As for the next big contract negotiation Dallas will have to get through with defensive superstar Micah Parsons ... Pearson says he's confident that after Jerry Jones got Prescott and CeeDee Lamb's deals done -- Parsons' won't be far behind.