The victory saw United reclaim second place from city rivals Sheffield Wednesday who briefly went above them in the table with a 2-0 win at Huddersfield earlier in the day.
Early pressure from the home side saw Evans have a shot blocked and Kevin McDonald fire over from a good position after playing a one-two with Cresswell.
United took the lead after 34 minutes when Matt Lowton’s cross was knocked down by Cresswell and Evans volleyed in from around eight yards out for his 32nd goal of the season.
Evans turned provider five minutes after the break when his low cross from the byline found Cresswell who bundled the ball over the line from close-range.
Bournemouth pulled a goal back when Zavon Hines showed good anticipation to block a throw out from goalkeeper Steve Simonsen before rolling it into the empty net. Referee Andy Woolmer allowed the goal to stand amid strong protests from the Blades.