On a sweltering evening in the Thai capital, Mourinho watched his senior players get their first proper run-out of the pre-season campaign.
The only goal of the game was scored from the penalty spot by Romelu Lukaku on 34 minutes.
Mourinho's first-half line-up featured new signings Wallace at right-back and Andre Schurrle on the left side of an attacking midfield three.
Both those players impressed in the opening 45 minutes, which included a drinks break midway through due to the humidity at the Rajamangala Stadium.
The introduction of Eden Hazard after the break gave the Chelsea attack some much-needed pep, while new-boy Marco van Ginkel showed discipline in his use of the ball in midfield.
Giroud, who had scored a brace in the Gunners' 7-0 romp over an Indonesian Dream Team at the weekend, put the tourists ahead inside five minutes after collecting a pass from Tomas Rosicky.
Arsenal - with Bacary Sagna deployed at centre-half - had to wait until just before the break to further extend their lead, as Lukas Podolski saw an effort chalked out for offside and then hit the post.
Giroud eventually made it 2-0 on 44 minutes, and then completed his treble with another neat finish from Alex Oxlade-Chamberlain's pass after Anh Duc had missed the home side's best chance.
Following the restart, England midfielder Oxlade-Chamberlain slotted in number four after being set-up by Theo Walcott.
After a number of anticipated substitutions, England under-19 international Chuba Akpom scored a quickfire double (56, 59), the 17-year-old having replaced Giroud.
England midfielder Jack Wilshere then made his first appearance of the tour after he came on for Oxlade-Chamberlain just after the hour mark.
With 15 minutes left, defender Ignasi Miquel converted number seven after a powerful run and cross from attacking German midfielder Thomas Eisfeld.
Darron Gibson gave Everton an 11th-minute lead, slotting in from a corner.
Victor Anichebe headed home a second from Kevin Mirallas' cross five minutes later.
Mirallas got on the scoresheet himself with a fine free-kick a minute before the break, but the hosts pulled one back on the stroke of half-time through Peter Murphy.
Leon Osman headed home a fourth for Everton shortly after the hour mark as they ran out comfortable winners.
Rodriguez broke the deadlock in the friendly in Palafrugell on the Costa Brava in the 28th minute, having earlier had a goal disallowed.
The striker took advantage of a defensive mix-up to score.
The Saints conceded a headed equaliser to David Cano just after the hour mark, but Rodriguez won it six minutes later, scoring from a tight angle after Adam Lallana had a shot saved.
Rangers continued their pre-season preparations ahead of their forthcoming Second Division campaign with a 1-0 win over FC Gutersloh in Germany.
A first-half goal from skipper Lee McCulloch proved to be the difference between the two sides in a match where the visitors had a few decent chances.
The outing also provided new signing Arnold Peralta with his first Rangers appearance after the Honduran was thrown into the action in the second half.
Hearts managed to put their off-field troubles to one side to claim an emphatic 5-0 victory over Raith Rovers at Starks Park - their second pre-season win.
Kevin McHattie, Billy King, Jamie Walker, Ryan Stevenson and Gary Oliver all helped themselves to a goal apiece for the Jambos.
The Edinburgh side had also defeated fellow administration-hit outfit Dunfermline at the weekend.
Inverness secured a comfortable 4-0 win over Highland rivals Clachnacuddin.
The match remained deadlocked at the interval but a double from Calum Ferguson and goals from Ryan Christie and Jason Brown in the second half saw Caley Thistle run out 4-0 winners.
The clash between Kilmarnock and East Fife was a closer affair, with trialist Ryan Harper grabbing the only goal of the game at Bayview.