Coyle left Burnley in acrimonious circumstances in January 2010 and was the recipient of a feisty reception from the Clarets faithful on Bolton's first game in the Championship since relegation from the Premier League.
The intensity was matched on the field as Burnley more often than not enjoyed the better of a contest played at a ferocious pace.
Paterson emerged as the beneficiary of a goalmouth scramble six minutes before half-time to open the scoring and strike partner Austin pounced from close range to seal the points.
Bolton centre-back Zat Knight had a late header cleared off the line but Coyle was left with plenty to ponder as Bolton's bid for an instant return to the top flight got off to a poor start.
Paterson replaced summer signing Brian Stock in the only change to the Burnley side that triumphed 3-1 at Port Vale in the Capital One Cup on Tuesday night.
Keith Andrews was a debutant in a Bolton team featuring former Claret Tyrone Mears, making only his second appearance for the club following an injury nightmare last term.
Coyle was welcomed to the dugout with chants of "Judas" from the home support and Burnley midfielder Chris McCann might have cranked the pressure up further in the opening moments when his lashed over from the edge of the box.
McCann's chance came courtesy of Bolton's Tim Ream failing to win a defensive header and the American centre-back's inauspicious start continued when Paterson stole in behind him and placed a clever lob onto the roof of Adam Bogdan's net.
In the 22nd minute Ross Wallace's corner fell kindly for Austin who missed his kick, allowing Bolton to spring up the other end where Lee Chung-Yong scuffed wide following an excellent run by Marvin Sordell.
Bogdan was forced to palm Dean Marney's well-struck drive to safety and shortly after the half-hour Wanderers winger Martin Petrov fizzed a volley narrowly over the crossbar.
Burnley appeared to be carrying the greater threat, though, and duly took a 39th-minute lead - Paterson heading home from close range amid chaos in the Bolton area after goalbound shots from Junior Stanislas and Marney were blocked.
The hosts were in the ascendancy once more when the action resumed as McCann and Austin prompted some uncertain handling from Bogdan before the latter doubled his side's advantage.
Stanislas' cross from the left wing was perfectly measured to leave the former Swindon striker with a simple 57th-minute finish at the back post.
Bolton might have fallen further behind shortly afterwards when Paterson found space down the inside-right channel and forced Bogdan to turn a shot behind.
In the 65th minute, Burnley full-back Joseph Mills curled a cross towards Austin, whose header was blocked by Ream before Paterson planted the rebound over.
Wastefulness in the final third prevented Bolton fashioning any clear opportunities in response until Knight's header from Chris Eagles' corner was cleared off the line by Burnley substitute Ben Mee.