But they then lost just two of the next 14, not only charging into play-off territory, but also securing a prized home tie against European Challenge Cup finalists Bath.
In the five previous seasons of Premiership play-offs, Wasps claimed three titles, suggesting that Bath have got their work cut out at Adams Park.
McGeechan though, knows Bath's current form and high-tempo style of rugby makes them dangerous opponents.
"We are in the play-offs now, and the stakes have risen accordingly," he said.
"In Bath, we are playing a side that is probably the most consistent all season. They are well-coached and play good rugby, which will challenge us in all areas.
"We will have to have every part of our game working well if we are to come out with a win."
England wing Paul Sackey, who limped off during the victory over Leeds last weekend, has been named in Wasps' starting line-up but faces a late fitness test.
Bath, meanwhile, have seen England front-row forwards Lee Mears (shoulder) and Matt Stevens (knee) restored to full fitness following their early departures during an 8-6 defeat at Gloucester seven days ago.
The Gloucester loss cost Bath a home semi-final, and head coach Steve Meehan said: "What we have to work on from last week is our selection in regards to where we go and attack.
"We have to try and shift the ball, be comfortable on the ball and make sure we recycle well and find a space.
"Of course, apart from that, it is a matter of concentrating and playing for the 80 minutes.
"I truly believe that if we had played the second-half in the same way that we played the first, we would have ended up winning that game against Gloucester.
"We know our game. It's just a question of believing in it and seeing it through. If we execute it as well as we can, we are a difficult team to stop."
Table-toppers Gloucester, a feat they have now achieved three times in six seasons, are favourites to make home advantage count against reigning Premiership champions Leicester.
Gloucester head coach Dean Ryan has named an unchanged team following the Bath game after Mike Tindall, Anthony Allen and Akapusi Qera all recovered from knocks.