Airey made six superb turnovers to help prevent Bath from making any significant inroads in their lead as Rhinos avenged their 20-goal defeat from earlier in the season.
Rhinos took an early lead thanks to excellent work from Sigi Burger and Brie Grierson. Bath battled back to level matters but Grierson helped Rhinos forge ahead again at the end of the first period (17-14).
It was nip and tuck in the second period but Leeds held on to their four-point lead at 35-31 at half-time.
With Vicki Oyesola, Lydia Walker and Jade Clarke hitting form and some great shooting from Burger, the Rhinos increased their lead to 48-40 at the end of the third quarter.
Rhinos held their nerve in the final quarter and with Clarke and Airey on top form, they held on for an important victory.
On Saturday, Rhinos slipped to a 55-51 defeat to lowly Celtic Dragons.
Burger and Brie Grierson combined well to score 14 goals between them as Leeds took a 16-14 lead into the first break.
But the Dragons fought back in the second quarter with Georgia Rowe impressing up front with a 100 per cent shot-success rate as Celtic drew level at the half-time break.
The Dragons took the lead for the first time in the third quarter but it was Rhinos who regained the edge, scoring 12 goals to the visitors’ 11 as the Yorkshire side took a one-goal lead into the last 15 minutes of the match.
Dragons then upped the ante and Shaquanda Greene-Noel made an impressive 11 turnovers, severely limiting the service into Burger.
This, together with an inspiring display from Nia Jones saw the Dragons take the lead with five minutes to play – a lead they were never to lose.
Rowe kept the scoreboard ticking over, scoring 40 goals in total as the Dragons eased to victory.