To make matters worse for the Broncos their star prop Payne Haas was seen limping badly at the end of the match at Suncorp Stadium.
Moses was on fire in his return from injury with winger Zac Lomax his powerhouse self with two cracking tries.
The clash had a drama-charged finish when Brisbane fullback Reece Walsh was off-side when collecting a Gehamat Shibasaki grubber with 48 seconds left on the clock.
Parramatta fullback Joash Papalii was a sensation at No.1 and was a relieved man when Walsh was denied after he knocked-on for his opposite number to swoop.
The Broncos, at full strength and on the back of five wins in a row, were error-riddled in the second half with Walsh the worst offender in a rocks and diamonds display.
The home side led 14-12 at halftime against an Eels side that were more than up for the fight.
Both halfbacks, at the elite end of the spectrum most weeks, were highly influential.
Moses, back from a calf injury sustained in NSW camp in the lead-up to game two of the State of Origin series, was superb with his long and short kicking game to set up two tries.
Broncos counterpart Reynolds was also on song with a runaway intercept try and crafty inside pass for Kobe Hetherington to race away.
Moses was at it again after the break with a lovely out ball to Will Penisini to send Lomax over for his second after a loose pass by Walsh gifted possession.
Walsh took several poor options in attack before on the last tackle he put on a superb step on the 40m line and found bench specialist Billy Walters in support to give Brisbane a 20-18 lead.
Addo-Carr would not be denied and streaked over for his 150th career try to grab the lead
The hosts left Haas on the bench for 30 minutes in the middle of the match as he battled a lingering lower back complaint, but he came back on for the final stint before suffering another possible injury.
The first half was full of quality and competitive footy.
Brisbane forward Xavier Willison was put on report for a cannonball tackle on Eels prop Junior Paulo early and the visitors got into a grind with determination.
Walsh made the cardinal error of letting a Moses mid-field bomb bounce. Parramatta centre Sean Russell gathered, chipped over Walsh's head and scored a cracker.
Reynolds then swooped on a Dean Hawkins pass to race 75m to score.
The captain orchestrated the next try for Hetherington but the visitors were plucky.
The quality of the Eels attack has improved markedly over the season and Moses, with a set play, lobbed a perfect kick for aerial specialist Lomax to dive, catch and score.
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