It was the second time in five days that the Senegal forward has proved decisive after his late strike against PSG put Chelsea into the Champions League semi-finals.
"We played in the Champions League in the week, and it was a physically and emotionally draining game," the assistant coach, standing in for manager Jose Mourinho, told the BBC.
"It was difficult to go again, but we stuck to it and came through," Holland added.
Sunday's victory moved Chelsea to 75 points, two behind Premier League leaders Liverpool, who they play in a potentially decisive clash on April 27, and five ahead of third-placed Manchester City, who have two games in hand.
Chelsea were lethargic for large periods in south Wales and struggled to break down a stubborn Swansea side whose task was made much more difficult when Flores was sent off after receiving two early bookings.
The London club finally made the breakthrough in the 68th minute when Ba, rewarded with a rare start after his Champions League heroics, hit a low shot that bobbled past Swansea keeper Michel Vorm.
"I've been here three times with Chelsea without winning before today," Holland said. "Swansea can frustrate you. They're good at retaining possession.
"With the game at 0-0, they've got everybody behind the ball every minute of the game. You've got four defenders, four midfielders and one attacker to get through.
"We had total control of the game, but still had to find a way through. When you do that, the spaces are there."
Captain John Terry said their patient approach after the sending-off proved crucial.
"Patience was the key today," he told Sky Sports. "We were not always patient and at our best but it was an important three points."
After Liverpool moved firmly into pole position in the title race with a 3-2 win over Manchester City earlier on Sunday, Terry chose to copy manager Mourinho by saying the pressure was on their rivals heading into the final games of the season.
"Looking at the (Liverpool) result it was probably the one we wanted even though Liverpool are flying. The pressure is still on the teams above and below us," he added.
"It will be very tough, but it's important we keep winning our games. It's out of our hands. We need City to lose or draw and we've still got to go to Anfield. It's going to be a great end to the season."
- Sports & Recreation
- Premier League
- Chico Flores
- Manchester City
- Jose Mourinho
- Demba Ba