The one-point victory ensured Exeter will play Heineken Cup rugby again next season, along with Gloucester, with Bath’s loss to Saracens made irrelevant.
Exeter scored the opening try after six minutes as lock Dean Mumm scored, with Steenson adding the touchline conversion followed by a 40-metre penalty.
Exeter pressed the Gloucester line with a break from Mumm, who fed lock Damian Welch, who touched down. Steenson was off target with the conversion but then added a 20-metre penalty.
Gloucester finally got points on the board after 20 minutes through a penalty from fly-half Freddie Burns, followed by their first try through Jonny May who burst 45 metres down the touchline.
With ten minutes of the first half remaining, another Exeter error led to Burns breaking from his own half and, with a man over, fed lock Lua Lokotui who shipped the ball to winger Charlie Sharples, who fired his afterburners to score Gloucester’s second try, Burns adding the extras.
Henry Trinder added the Cherry and White’s third with an interception try after a mistake from Scaysbrook.
But Exeter regained the lead on the stroke of half time after Steenson’s conversion put the Chiefs 25-22 ahead.
The Exeter fly-half increased the Chiefs lead with three penalties in the opening 15 minutes of the second period. Gloucester woke up midway through the half with full-back Rob Cook crossing in the corner for the bonus point try.
Burns added the conversion and a 30-metre penalty to reduce the arrears to two points with 17 minutes remaining, but Steenson added his sixth penalty.
Burns then squeezed in the corner for Gloucester’s fifth try before adding the conversion.
Steenson was short with his touchline penalty before full-back Luke Arscott sliced a drop goal. Steenson redeemed himself to kick the points which sealed victory and European rugby.
n Christian Wade took his tally to 13 Aviva Premiership tries but could not prevent Wasps from going down 21-20 to Sale at the Salford City Stadium. Neither Sale nor Wasps were playing for anything other than pride, but they served up an entertaining first half as the hosts took a 12-7 lead.
Tom Varndell – aided by ten points from the boot of Tommy Bell – gave Dai Young’s men a 20-18 advantage late on.
But Macleod kicked a three-pointer five minutes from time to snatch the win.
n Saracens ensured they finish top of the Aviva Premiership regular season standings with a hard-earned 23-14 victory over Bath.
The home side were nowhere near their best, but still did enough to gain a home semi-final against Northampton next weekend following tries from England internationals Chris Ashton, Mako Vunipola and Owen Farrell.