Reds took a 2-0 lead in the first half through goals by Enzio Boldewijn and Mark Randall.
But then nearly 15 minutes after the start of the second half they conceded a freak goal when Josh Payne tried to clear but instead the ball bounced off Jimmy Smith and flew back into his own net for an own goal.
Kewell was pleased his side dug-in and saw out the game under pressure from the visitors.
After defending well, Crawley attacked on the break and nearly made it 3-1 when Lewis Young broke clear with just ‘keeper Aaron Chapman to beat, who produced a vital save to deny him a goal.
Kewell added: “It was important we reacted in the same way that we did when we played against Notts County, and I felt we did that.
“Accrington are a very good team; John (Coleman, manager) has them playing in the right way; we always knew it was going to be a football game.
“The last couple of games we’ve seen things that you don’t usually see in football and it’s how you react to it.”
Kewell praised Boldewijn for his match-winning display.
He said: “I thought he was exceptional the whole game. He scored a sensational goal and to assist for the second it was a superb day.
“Strange things happen in games at certain moments and I thought we reacted in the right way.”
Kewell also heralded striker Thomas Verheydt for his contribution to the victory.
He said: “I thought it was an excellent performance in a very tough, physical game, especially in the second half he was having to play closely by himself.
“He still dominated and was creating chances; he just needs that goal like any striker. If he keeps doing his job like it will be fantastic.”