Whelan struck from inside the area on 43 minutes to put Town in front at the break and they showed great character to dig deep for all three points when George Carline was shown a second yellow card with eight minutes to go.
The win moves the Blues up to 16th.
Here are Liam Norcliffe’s player ratings from the game...
1. Kyle Letheren 7
Five clean sheets on the bounce for Letheren which is a great achievement. He made a crucial stop early in the game to deny Solihull's Cameron Archer. Recovered from a clash of heads in the first half which was a relief with no sub goalkeeper on the bench. Photo: Dean Atkins
2. George Carline 8
A solid and impressive showing from Carline who won a number of tackles for Town. Almost grabbed an assist when his cross was met by Denton but his header was saved. Harshly sent off late on for two yellow cards. Suspended for the next match. Photo: Dean Atkins
3. Will Evans 7
Hardly put a foot wrong in the difficult conditions. Improving week-by-week. Photo: Dean Atkins
4. Haydn Hollis 7
A no-nonsense display. Continues to mop up at the back and is showing great calmness on the ball. Photo: Rachel Atkins