Connolly spent the second half of last season on loan at Luton Town, but he picked up where he left off with Albion last term.
A hamstring injury made for a frustrating time with the Hatters, but an explosive first half to the season with the under-23s saw him plunder 17 goals in 18 games, winning the Premier League 2 Player of the Season Award in the process.
Those goals helped Simon Rusk’s side to an impressive third-place finish, but this season could prove tougher, with a number of the clubs' under-23 players out on loan.
Six of his potential squad are now playing in the Championship, League One, and in Germany’s Bundesliga 2 — where Leo Ostigaard and Victor Gyokeres are with St Pauli.
Nonetheless Rusk’s side still had a familiar look to it, with summer arrival Taylor Richards the only new signing on display following his switch from Manchester City last month, playing just off Connolly.
Striker Connolly and Steven Alzate had been at the Amex earlier in the day, and included in the club’s first-team photoshoot. Along with Romanian international Tudor Baluta, the pair have been training with the first team, under new head coach Graham Potter.
Alzate spent most of last year with Swindon Town, before injury curtailed his season and he returned to Albion. Anders Dreyer was also back, following a loan stint north of the border at St Mirren in the second half of last season, and started on the right.
Albion looked good in possession, but found hard-working Wolves difficult to break down. Their stubborn resistance limited Albion during the first half, to a half-hearted penalty shout, as Connolly went to ground after a clever chipped pass by Alzate, and a free kick by skipper Max Sanders which went wide of the right post.
The first real opening for Albion arrived 12 minutes after the break, as Richards got a sight of goal, but Dion Sanderson made an excellent block. Max Sanders followed up with a shot which was well saved by Andreas Sondergaard, before Dreyer stabbed the loose ball over the bar.
Tom McGill then made a superb save at the other end to keep the scores level and deny Taylor Perry at close range. The Albion keeper dived full length to push the ball away to safety, after the Wolves wide man had got a good first-time connection on John Kitalano’s cut back from the left touch line, and with Wolves enjoying their best spell of the game, Ed Francis struck the foot of the right post with a free-kick from the edge of the box.
With less than 20 minutes left to play, Albion regained control of the game, turning up the heat on the newly-promoted side.
Sanderson was on hand to make another fine block, this time denying Haydon Roberts, after Warren O’Hora had headed down from a corner — but the impressive Wolves defender could do little to stop Connolly opening his account for the season from the following corner.
The prolific striker was quickest to a loose ball, after Roberts had fired in another effort, and Connolly showed his prowess as he smashed it into the roof of the net.
Within two minutes Connolly had helped himself to his second of the contest, running onto another lovely chipped through ball from substitute Jordan Davies, and instinctively lifting it over the on-rushing Sondergaard and into the net.
That was enough to seal a victory on the night, and the side can now look forward to Friday night’s game away to Arsenal in confident mood.
Albion line-up: McGill (GK); A.Davies, O'Hora, Roberts, Cox; Sanders (C), Richards (J.Davies 73), Dreyer (Longman 87), Alzate, Cochrane (Gwargis 46); Connolly.
Subs not used: Debois (GK), Radulovic.