The pair spent most of last week on international duty together with Michael O'Neill's Northern Ireland side, who were held to a 0-0 draw in Malta on Wednesday.
This weekend went much better for them both, though, with Davis scoring as Southampton impressively defeated Manchester City 3-1 on Saturday evening.
That result meant Evans' United side could open up a 12-point gap at the top of the Premier League, which they duly did with victory over Everton.
"He said to me throughout the week that it would be nice to try and get a result for him," Davis said. "Obviously that's not something I worried about but it is always nice to help an international team-mate."
Davis was more concerned with the fact Southampton managed to secure a first win under new manager Mauricio Pochettino, moving them four points clear of the drop zone.
"We're obviously delighted with the result," he said. "We knew we would obviously have to put a lot of pressure on them up the pitch.
"That is the way the manager wants us to play and we managed to do that. We caused them a few problems and deserved the three points.
"It is hard to look at other teams at this point in time. You've just got to concentrate on yourself.
"We've shown that if we can keep the consistency going and level of performance we are more than capable of staying in this division and hopefully kicking on."