Having secured pole position on Saturday afternoon, double BTCC champion Turkington produced a lights-to-flag performance in Sunday's opener.
The Ulsterman made a strong getaway and was able to resist the attentions from Tordoff's Team JCT600 with GardX BMW in the early running, before gradually stretching his lead in the latter stages.
It's an historic result for the Japanese marque, which had so far endured a baptism of fire on its introduction to Britain's biggest motor sport series.
Challenging weekends at Brands Hatch and Donington Park were followed by the difficult decision to withdraw from the race day at Thruxton last time out, amid safety concerns with its fuel system.
New components, engine modifications and a two-day pre-event test seemingly had the desired effect on the all-new Levorg model, as Turkington's success was bolstered by a hat-trick of podiums for team-mate Jason Plato.
The BTCC's most winningest driver finished third in Cheshire's curtain-raiser as the two Subarus sandwiched Tordoff's West Surrey Racing BMW 125i M Sport for the podium positions.
Tordoff then ignited his championship charge with his first victory of the season in race two – incredibly becoming the ninth different driver to win a race so far in 2016.
The BMW blasted off the line, past pole-sitter Turkington, and never looked back. The unpredictability of this BTCC campaign continued as the Yorkshireman romped home to add his name to an ever-growing list of race-winning drivers.
Turkington and Plato finished second and third to make it a brace of double podiums for Subaru in the first two bouts. Halfords Yuasa Racing's Gordon Shedden and Speedworks Motorsport's Tom Ingram finished fourth and fifth respectively.
The result also fired Tordoff to the top of the standings, despite being only sixth in the table at the start of Oulton Park's proceedings.
Tordoff and Neal then pulled further clear in the championship table after securing the first two podium positions in the final race of the day, with the latter taking a quite dominant victory.
Honda originally looked in place to notch a one-two finish after Shedden muscled his way past MG Racing RCIB Insurance's Josh Cook on the opening lap. The two bright orange Civic Type Rs immediately pulled away from the rest of the field, but reigning champ Shedden was never close enough to challenge his team-mate. Disaster struck for the Scotsman on the penultimate lap when a puncture, after apparently hitting a kerb, forced him out of contention.
Cook – already reeling from the earlier attack by Shedden – was now embroiled in a fairly heated debate with Tom Ingram's Toyota, as the pair tapped and nudged their way through the entire contest. The battle would eventually play into the hands of the experienced Plato, who snatched the final spot on the rostrum in dramatic fashion.
Ingram was edged onto the grass as the gaggle of cars ran down to Lodge for the final time. The Speedworks star was determined not to let Cook past, but in holding up his rival he merely opened the door for the Silverline Subaru BMR Racing car to run around the outside and steal the advantage.
Despite being shuffled slightly down the order, young gun Ingram still went on to take his third Independents' victory of the day – matching his best ever weekend points haul in the process.
Tordoff tops Neal by just one point in the overall championship, with both drivers now pulling clear of the chasing pack headed by Shedden and Rob Collard.
Collard made his final move of the weekend on the run to the chequered flag, rounding off a staggering display from the Team JCT600 with GardX driver. The experienced racer had seemingly carved his way through the field in each of the Oulton Park races, but misfortune had up to that point prevented him from scoring a real result. He would not be denied in race three, however, as he stormed from 25th to sixth – beating Turkington's Subaru to the line by just 0.041s.
West Surrey Racing leads the Manufacturers'/Constructors' points tally, whilst Team JCT600 with GardX top the HiQ Teams' table.
Despite a relatively low key weekend for Motorbase Performance it still left the Cheshire track in command of the Independent Teams' title, and its talent Andrew Jordan heads the Independent Drivers' standings.
MG Racing RCIB Insurance driver Ashley Sutton maintained his advantage in the Jack Sears Trophy.
The Dunlop MSA British Touring Car Championship now moves on to Croft in Yorkshire in two weeks time (18/19 June).
Jason Plato was reprimanded and received a verbal warning for leaving the track and failing to rejoin safely.
Jeff Smith was remprimanded and received two penalty points for an incident involving Rob Collard.
Martin Depper was reprimanded and verbally warned for an incident involving Rob Austin.
Jason Plato was reprimanded and fined a sum of £500 and received three penalty points for an incident involving Daniel Lloyd.
Silverline Subaru BMR Racing was fined a sum of £500 for having tyre trollies on the grid in contravention of championship regulations.
Rob Austin was reprimanded and received two penalty points for an incident involving Jake Hill.