"We were the aggressors," Davis said after the 114-108 win Thursday at the ESPN Wide World of Sports Complex inside Walt Disney World Resort.
"We were more physical. They were the aggressors and the more physical team in Game 3, and we came out [Thursday] and played our style of basketball pretty much for the entire 48 minutes."
LeBron James also filled the box score with 26 points, nine rebounds and eight assists in the Game 4 win.
The four-time NBA MVP also requested the defensive assignment of Nuggets sharpshooter Jamal Murray. Murray scored a team-high 32 points, but failed to make a 3-point attempt in the loss.
"I knew it was winning time, and Jamal had it going," James said.
Davis scored 13 points and James scored 10 points in the first quarter to lead the Lakers to a 37-30 advantage. Dwight Howard -- who started at center for the Lakers -- chipped in eight points in the first 12 minutes.
Nikola Jokic scored eight points in the second quarter to help the Nuggets cut the Lakers lead to 60-55 at halftime. The Nuggets outscored the Lakers 29-27 in the third quarter, but still trailed 87-84 at the start of the fourth frame.
The Nuggets cut the Lakers lead to 87-86 in the first minute of the fourth quarter, but could never tie the score or take a lead down the stretch. The Lakers responded to the lead trim with a 9-2 run to secure the victory.
Howard had 12 points and 11 rebounds for the Lakers. Kentavious Caldwell-Pope chipped in 13 points in the win. Rajon Rondo had 11 points, seven assists and five rebounds off the Lakers bench.
Jokic had 16 points, seven rebounds and four assists in the loss. Jerami Grant scored 17 points for Denver. Michael Porter Jr. had 13 points and eight rebounds off the Nuggets bench.
"We just had so many breakdowns throughout the game," Murray said. "We've just got to be better. We can't give them that many second-chance points while we're having breakdowns.
"We've just got to be better [and] give ourselves a chance."
Davis, who also had five rebounds, three assists and three steals in the win, rolled his ankle in the fourth quarter, but said he was "fine" during his postgame news conference.
Game 5 of the Western Conference finals is at 9 p.m. EDT Saturday in Orlando. The Lakers could clinch a trip to the NBA Finals with a win.