Newly-capped England fly-half Freddie Burns opened the scoring for the hosts with a penalty, which was matched by Tom Homer.
However, that proved to be the only points of the game for the Exiles, as Gloucester ran riot.
Monahan crossed twice in the space of five minutes before half-time to put Gloucester in charge. Full-back Rob Cook added a third score three minutes into the second period before Monahan completed his hat-trick and secured his team's bonus point.
Burns kicked a total of 17 points while Monahan helped himself to a fourth try before scrum-half Dan Robson completed the rout to move Gloucester closer to a quarter-final berth.
Bath are also one win away from booking their place in the knockout stages following a comfortable 39-5 win over Calvisano.
Gary Gold's team ran in seven tries, including a hat-trick for Horacio Agulla, in snowy northern Italy to move eight points clear at the top of Pool Four.
The snow was cleared from the pitch and Simon Taylor crashed over for the first try after just three minutes.
Agulla then scored twice before Tom Biggs grabbed the bonus point before half-time.
Jack Cuthbert and replacement Mark McMillan touched down for second-half scores as the visitors continued to dominate.
Hooker Luigi Ferraro crossed for a late consolation for the hosts but it was Agulla who had the last word to seal an impressive display as Bath continued their unbeaten campaign.
London Welsh's first season in Europe was ended at the pool stage after they slipped to a 27-13 defeat against Grenoble at the Kassam Stadium.
The French club put their off-field troubles aside with a bonus-point victory that left runaway Pool Five leaders Stade Francais Paris eight points clear and with one foot in the quarter-finals.
Grenoble, stripped of the points from their 20-9 result in round three after being found guilty of fielding an ineligible player, took the lead with a penalty goal from Valentin Courrent and the scrum-half quickly added a conversion.
That kicking opportunity came courtesy of hooker Laurent Bouchet crossing the Exiles' line and the front-row proved that was no fluke when he added another eight minutes later.
Fly-half Alex Davies kept London Welsh in the game up to the break with two penalties but the gap was quickly restored two minutes into the second half when Florian Ninard touched down.
Replacement flanker Mike Denbee crossed for an Exiles try that Davies converted, but Feliuaki Taukeiaho claimed a bonus point six minutes from time.
Spanish minnows Bizkiaia Gernika claimed a second successive win in their debut season, 16-10 at Rovigo in Pool Two.
It could not be tighter at the top of Pool Two and it was honours even - five points each from their back-to-back contests - after Perpignan ground out a 13-6 win against Worcester Warriors at Stade Aime Giral which left the clubs locked together on 15 points.
Both clubs will have rematches with Bizkiaia Gernika RT and Femi-CZ VEA Rovigo in the new year and it could all come down to who performs best - and picks up bonus points - in those games to determine who goes through to the last eight as pool winners.
Andy Goode, who contributed all the Warriors' points in their 22-21 win at Sixways in round three, scored the Aviva Premiership club's only points of a tense and tight first half with a 35th-minute penalty.
The only try of the opening 40 minutes came after eight minutes, when wing Richard Haughton cracked the Worcester defence. The boot of Wales star James Hook did the rest of the damage in the first half with the conversion and penalties on 33 and 37 minutes.
It stayed on a knife edge into the second 40 minutes.
Goode was on target with another penalty as both teams made a raft of replacements, but the fresh legs could not get Worcester back into the game.
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