MIDDLESBROUGH, England — Southampton strengthened its chances of securing a top-half finish in the English Premier League by beating already relegated Middlesbrough 2-1 on Saturday.

Jay Rodriguez made the most of a rare start to score in the 42nd minute for Southampton, and substitute Nathan Redmond added a second in the 57th with a curling shot into the top corner.

Shane Long wasted a chance to make it 3-0 when he smashed a penalty that struck the crossbar and flew over in the 64th but it didn’t make a difference, even though Patrick Bamford replied for Middlesbrough by heading home from a corner in the 72nd for his first Premier League goal.

Southampton climbed into ninth place, with two games left.

Middlesbrough’s relegation was confirmed on Monday when the team lost 3-0 at Chelsea.