Ibrahima Traore fired Borussia into an early lead before Matt Grimes, celebrating his 20th birthday, pulled the Swans level.
Monchengladbach, who qualified for this season’s Champions League after finishing third in the Bundesliga, have played two more games than Swansea during pre-season but struggled to contain the Welsh side who dominated possession for long spells.
On a scorching day in South Germany, Swansea boss Monk named a strong lineup with Ashley Williams, Gylfi Sigurdsson and Batefimbi Gomis all starting alongside new-boys Andre Ayew and Franck Tabenau.
They were not able to stop Borussia taking the lead in the 14th minute, though, as Ibrahima Traore cut in from the right to curl a perfectly hit left-footed shot into the top corner.
Falling behind spurred the Swans into action as they dominated possession for the remainder of the first half with their typically fluid brand of passing.
However the domination was not repaid with a goal and their best chances came, somewhat surprisingly, from set pieces – Kyle Bartley and Batefimbi Gomis both heading over the bar before the halftime whistle sounded.
At the start of the second period Monk opted for continuity and made no substitutions, but when the changes finally arrived there were no half measures. The Swansea manager rotated the entire starting 11 for the remainder of the second half, handing debuts to Eder and Kristoffer Nordfelt.
The decision provided a valuable injection of energy – as the intense heat had already forced several drinks breaks – and Monk was immediately repaid for his radical alterations with a goal.
The lively Wayne Routledge charged to the by-line before pulling the ball back for young midfielder Matt Grimes to poke the ball into the back of the net under significant pressure from the Borussia defence.
Looking for a winner, the Swans again ended the half strongly with greatly superior possession, but were unable to convert the few chances they carved, which fell to new-boy Eder and the goal-shy Marvin Emnes.
Speaking after the game, Monk was delighted with his side’s performance.
“I thought for our first game we did very well. We dominated the game, and to do that against an opponent who has already played two games before this match was very pleasing,” he said.
“It’s always difficult to play in heat like that, but I thought we handled it very well. Our fitness levels continued to be strong and we finished the game the stronger of the two teams.
“Of course, there are things we can improve on – which we will do. In the first 15 minutes we could have done a little better, but after that we really came into our own and dominated the game. But I suppose it is understandable considering we were back in a game environment for the first time in a few months.
“In the second half we always looked a threat; got the deserved equaliser and were a little unlucky not to get a winner.
“I’m never totally satisfied – there are always things to work on – but we saw good things, fitness-wise especially as we finished the game strongly.
“We can be sharper with the ball, but we did move it around well at times. We could see what we’ve been working on coming through.
“I am pleased with this result but the players realise there is plenty more work to be done.’’