Setting up his second of the afternoon, Moloney played a superb ball through to Sam Baldock and the striker left the Boro defenders all in a line looking at each other as he finished low past Day with the goalkeeper closing him down.
It was fast becoming the Day Show, however, and when Tyrone Barnett got his head on to the end of a cross from the left Day once again got down to his left to flick the ball away from danger.
Stevenage made five changes from the side that lost at Sheffield United on Friday, and while Francois Zoko was missing from the squad there was a starting place for Rohdell Gordon who had made his debut at Bramall Lane.
Michael Doughty shot well wide from distance, but the hosts were soon on the back foot again as Wade Elliott played in Baldock only for the striker to be denied once more by the legs of Day.
In what was an abject display from Graham Westley's men in front of their own supporters, Stevenage failed to show enough guile in the final third while at the same time gifting their opponents far too many chances in their own.
Stevenage: Day, Wedgbury (N'Guessan 84), Hartley, Mousinho, Jones, Heslop (Akins 39), Doughty, Freeman, Smith, Gordon (Okenabirhie 63), Burrow. Subs: Arnold, Flanagan, Banvo, Henderson.
Okenabirhie had smacked one shot high and out of the ground since his arrival, but his next was low but hit a body in the box. Akins also tried again, but his fierce shot was kept out by a defender getting in the way.
The league's top scorer, Sam Baldock, had an early sight at goal, but Boro keeper Chris Day got down well to his Reebok Brown Shoes
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Boro were pushing bodies forward leaving gaps at the back, and it was no surprise to see substitute Stephen Pearson net when Barnett exploited space in the Stevenage defence to play him in.
In the end City scored just the three goals when it could have been double that and although Luke Freeman got a late Reebok Kamikaze consolation for the home side, their fate had already been sealed.
There was a late consolation as Freeman curled in a wonderful free kick, but by that time Boro already knew that they would be playing League 2 football next season.
Akins went close not long after the restart, but his turn and low drive was drilled just wide of the far post.
Brendan Moloney was found out on the right by a ball, and after making his way down the touchline he hit a great, low cross to the far post where Elliott was waiting to tap in from close range.
Moloney almost had a third assist for the afternoon soon afterwards, but after playing in Barnett the striker scuffed his shot.
left to stop the effort from creeping inside his near post.
Boro made a change five minutes before half time with Simon Heslop making way for Lucas Akins, but just moments later the visiting Reebok Casual Shoes 2018
Bristol City: Moore, Moloney (Waggstaff 89), Nosworthy, Williams, Elliott (Pearson 73), Cunningham, Pack, Reebok Memory Tech Shoes
Barnett (Emmanuel Thomas 75), Gillett, Osborne, Baldock. Subs: Richards, Kelly, Reid, Burns.
side went ahead.
Boro then lost Gordon to injury, replacing him with another academy product, Fejiri Okenabirhie, and not long afterwards they went 2 0 down.
The striker then had a second chance after a good ball in from the left from Greg Cunningham but Day saved again, before moments later the Stevenage stopper made his third save in the opening eight minutes as he kept out a header from Derrick Williams from a corner.
Stevenage have been relegated to League 2 after they went a 10th consecutive match without a victory.
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